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1. Cardinal, Ordinal, And Nominal Numbers — FactMonster.com
Ordinal numbers tell the order of things in a set—first, second, third, etc. Ordinal numbers do not show quantity. They only show rank or position.
http://www.factmonster.com/ipka/A0875618.html

2. Cardinal And Ordinal Numbers - Online Language Quiz - UsingEnglish.com
cardinal and Ordinal numbers Choose the correct answer.
http://www.usingenglish.com/quizzes/240.html
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Quiz: Cardinal and Ordinal Numbers
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Choose the correct answer.
One Cardinal number
Ordinal number
Third Cardinal number
Ordinal number
Nought Cardinal number
Ordinal number
First Cardinal number
Ordinal number
We use numbers with dates. cardinal
ordinal We use numbers with names of kings and queens. cardinal ordinal We use numbers for hotel rooms. cardinal ordinal We use for floors of a building. cardinal ordinal cardinal ordinal We use numbers with names of popes. cardinal ordinal Click here for the answer sheet Statistics All Quizzes: Number of quizzes: New in the last 28 days: Public Quizzes: Public quizzes: Members' Area: Member quizzes: Register for free and gain access to additional quizzes Log In Register FAQ Don't Miss... Printable Versions Submit a Quiz English Tests ^ Back to Top ... Staff Page last modified: 25 November, 2007 16:19

3. German Numbers - Counting In German
For each number, two forms are shown (1) the cardinal number (Kardinalzahl 1, 2, 3 ) and (2) Ordinal number (Ordinalzahl - 1st, 2nd, 3rd ).
http://german.about.com/library/blzahlen.htm
zGCID=" test0" zGCID=" test0 test14" zJs=10 zJs=11 zJs=12 zJs=13 zc(5,'jsc',zJs,9999999,'') You are here: About Education German Language German Language ... Help
German Numbers: Counting in German
Cardinal and Ordinal Numbers, Dates
Kardinalzahlen, Ordinalzahlen,
Daten, Mathematik und Rechnen
Also see:
It's About (German) Time

Date and Time Glossary
German Math Terms (Rechnen) (below) Introduction - Einleitung
For each number, two forms are shown: (1) the cardinal number ( Kardinalzahl - 1, 2, 3...) and (2) ordinal number ( Ordinalzahl - 1st, 2nd, 3rd...). In some cases the fractional number ( Bruchzahl - 1/2, 1/5, 1/100...) is also given. (To make fractions [ ], just add - tel or - el to the number: acht el achtel [an eighth], zehn tel zehntel [a tenth].) Although the masculine (i.e., calendar date) form is shown for the ordinal numbers, they can also be feminine ( die ), neuter ( das ) or plural, depending on the noun they are used with: das erste Auto die ersten Menschen , etc. Listen to the Numbers in German!
null (zero, nought) For decimal numbers ( Dezimalzahlen ), German uses a comma (

4. Learn Spanish | Spanish Ordinal And Cardinal Number System
This learn Spanish grammar lesson is on Spanish Ordinal and cardinal numbers. It s pretty simple, just a case of having to memorize the Spanish words for
http://www.outerspanish.com/grammar/numbers.htm
LEARN SPANISH FOR FREE! Learn Spanish: Numbers Spanish Grammar
Subject Pronouns

The Verb
Ser
The Calendar
...
The Conditional Tense
Learn Spanish: Spanish Ordinal and Cardinal Number System This learn Spanish grammar lesson is on Spanish ordinal and cardinal numbers. It's pretty simple, just a case of having to memorize the Spanish words for each.
Ordinal Numbers
0. zero 101. ciento uno 1. uno 27. veintisiete 102. ciento dos 2. dos 28. veintiocho 103. ciento tres 3. tres 29. veintinueve 104. ciento sesenta y uno 4. cuatro 30. treinta 105. ciento sesenta y dos 5. cinco 31. treinta y uno 142. ciento cuarenta y dos 6. seis 32. treinta y dos 200. doscientos 7. siete 33. treinta y tres 300. trescientos 8. ocho 34. treinta y cuatro 375. trescientos setenta y cinco 9. nueve 35. treinta y cinco 400. cuatrocientos 10. diez 36. treinta y seis 500. quinientos 11. once 37. treinta y siete 600. seiscientos 12. doce 38. treinta y ocho 612. seiscientos doce 13. trece 39. treinta y nueve 700. sete cientos 14. catorce 40. cuarenta 800. ochocientos 15. quince 41. cuarenta y uno

5. Infinite Ink: Cardinal Numbers
The purpose of this page is to describe the different types of cardinal numbers. For an introduction to cardinal and Ordinal numbers see the ``Mathematics
http://www.ii.com/math/cardinals/
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C ARDINAL N UMBERS
A cardinal number is one way to measure the size of a set. Here is the definition used in Zermelo Fraenkel set theory (ZF): The cardinal (or cardinality ) of x, denoted card(x), is:
  • the least ordinal a equinumerous to x, if x is well-orderable, and
  • the set of all sets y of least rank which are equinumerous to x, otherwise. In ZFC all sets are well-orderable and only definition (1) above is needed. The purpose of this page is to describe the different types of cardinal numbers. For an introduction to cardinal and ordinal numbers see the ``Mathematics of CH'' section in my Continuum Hypothesis article
    Notation
    k l a is used for the Greek letter alpha and represents an ordinal; w is used for the Greek letter omega; aleph is used for the Hebrew letter aleph; and:
    • aleph is used for aleph-zero, the zero'th well-ordered infinite cardinal; aleph w
    • aleph w w w w w w x w
    • aleph a is used for aleph-alpha, the alpha'th (or a 'th) well-ordered infinite cardinal.
    Since all well-ordered cardinals are ordinals, sometimes I use ordinal notation for a cardinal or vice versa. For example, when I say k aleph k , the k on the left is being used as a cardinal and the k on the right is being used as an ordinal.
  • 6. SpeedWord For English Study - Cardinal And Ordinal Numbers (Flash 5 Required)
    An interactive quiz for studying English. It uses the Flash player plugin.
    http://www.manythings.org/wbg/numbers-sw.html
    This page requires the (free) Flash Player plug-in (Version 5 or Newer). Go to Word Based Games for ESL Students or Interesting Things for ESL Students Charles Kelly
    Frank McAree

    7. Cardinal And Ordinal Numbers - Learning English
    numbers Learning English. cardinal and Ordinal numbers - English. numbers - List cardinal numbers, Ordinal numbers
    http://www.englisch-hilfen.de/en/exercises/numbers/index.php
    Cardinal and Ordinal numbers - English
    Numbers - List

    Decide whether the following words belong to animals on the farm or wild animals . Write them into the correct column:
    eleven, eleventh, five, twenty-seventh, twenty-fourth, fourteen, twentieth, two, ninth, fifteenth Cardinal numbers Ordinal numbers
    Grammar Explanations

    Grammar Exercises
    Adjectives/Adverbs Articles ...
    Imprint/Contact

    Search the Website: Home Grammar Exercises Test your English Numbers var et_easy = 0; var et_ssl = 0; var et_pagename = "Cardinal/Ordinal Numbers - Exercises - Learning English"; var et_areas = "englisch Übersicht"; var et_ilevel = 0; var et_url = ""; document.write(lt+'script lan'+ 'guage="JavaScript1.3"> var et_js = 1.3;' + lt + '/script>' );

    8. French Numbers, Cardinal & Ordinal Numbers
    Speak7 helps you learn French numbers, French cardinal numbers, French Ordinal numbers, French Numerals, and more about French Grammar, French Vocabulary,
    http://french.speak7.com/french_numbers.htm
    Home Alphabet Adjectives Verbs ... More… French Numbers Salim 2006 © speak7.com I Like this Page Tell a Friend about this Page Save as Homepage You will learn in this lesson: French Numbers, Cardinal Numbers, French Ordinal Numbers. French Cardinal Numbers: French Numbers French Cardinal Numbers: Zéro Dix Vingt Soixante-dix Cent un Un Onze Vingt et un Soixante et onze Deux cents Deux Douze Vingt-deux Soixante-douze Deux cent un Trois Treize Vingt-trois Quatre-vingts Mille Quatre Quatorze Trente Quatre-vingt-un Deux mille Cinq Quinze Trente et un Quatre-vingt-deux Un million Six Seize Trente-deux Quatre-vingt-dix Un milliard Sept Dix-sept Quarante Quatre-vingt-onze Cinq cent quarante-trois Huit Dix-huit Cinquante Quatre-vingt-douze Neuf Dix-neuf Soixante Cent French Numbers are easy to learn, cardinal numbers are a piece of cake if you understand the logic behind them, from to 16 you will find unique words, that you just need to memorize as is. 17-18-19 are composed words meaning (10-7) (10-8) (10-9).(check the table above). So now you can easily count to 20. Numbers 21, 31, 41, 51...should have an extra “et” in between, it’s like saying (20 et 1) or (twenty

    9. Cardinal And Ordinal Numbers
    Two Ordinal numbers may have the same cardinality. For example, lots of Ordinals are countable. Define a cardinal number as an Ordinal number that does not
    http://www.win.tue.nl/~aeb/at/ordinals.html
    Cardinal and ordinal numbers
    Two sets are said to have the same cardinality when there is a bijection between them. This is a good definition. However, one would like to have a concept "cardinality" (rather than "the same cardinality"), so that one can talk about the cardinality of a set. The first proposal was: a cardinality is an equivalence class for the equivalence relation "having the same cardinality".
    Paradoxes
    Consider the Russell set Is it an element of itself? The answer is neither yes nor no, and this shows that mathematics does not remain consistent when it is allowed to define sets by arbitrary properties. Russell's solution was to introduce a hierarchy of types, so that a set whose elements are of some type itself has a higher type. That it is possible to set up all of mathematics in this way, starting from logic only, was shown in the famous treatise Principia Mathematica
    Sets and Classes
    A practical setup for mathematics, following the work of Zermelo-Fraenkel-Bernays-Gödel-von Neumann, is the following two-level system. One has sets and classes . Every property defines a class. A set is a class, but not every class is a set. The elements of a class are sets. Two classes with the same elements are equal.

    10. "numbers" ASL American Sign Language
    cardinal and Ordinal numbering cardinal numbers are the numbers you use for In ASL, Ordinal numbers 1 through 9 are done similar to cardinal numbers
    http://www.lifeprint.com/asl101/pages-signs/n/numbersordianlandcardinal.htm
    Cardinal and Ordinal numbers
    Numbers 1-10 1000 and up Fractions
    Cardinal and Ordinal numbering:
    Cardinal numbers are the numbers you use for counting: one, two, three...and so on.
    Ordinal Numbers are used to indicate position: first, second, third, fourth...and so on. In ASL, ordinal numbers 1 through 9 are done similar to cardinal numbers except they use a little twist of the wrist. Beyond "9th," ordinal numbers start adding a "TH" after the number instead of doing the twist. An interesting difference between English and ASL is that English uses the concept of "nd" for some numbers but ASL only uses "th." For example English uses 22nd but ASL uses 22th.
    Let's go over that again:
    Cardinal numbers are 1, 2, 3...
    Ordinal numbers, 1st, 2nd, 3rd...
    In ASL we do cardinal numbers 1, 2, 3, 4, etc.
    In ASL we do ordinal numbers:
    1 + twist
    2 + twist 3 + twist 4 + twist 5 + twist 6 + twist 7 + twist 8 + twist 9 + twist 10 + th (fingerspell "th")

    11. Do We Count From 0 Or From 1?
    Note the definitions 2 of Ordinal and cardinal numbers stem from the development There is a technical difference between cardinal and Ordinal numbers.
    http://kilby.stanford.edu/~rvg/ordinal.html
    Do we count from or from 1?
    The ordinal use of cardinal expressions
    ordinal number noun
    Date: 1607
  • a number designating the place (as first, second, or third) occupied by an item in an ordered sequence
  • a number assigned to an ordered set that designates both the order of its elements and its cardinal number cardinal number noun
    Date: 1591
  • a number (as 1, 5, 15) that is used in simple counting and that indicates how many elements there are in an assemblage
  • the property that a mathematical set has in common with all sets that can be put in one-to-one correspondence with it Note: the definitions 2 of ordinal and cardinal numbers stem from the development of set theory in the 19th century. The main motivation of these definitions is in the definition of infinite numbers. In the remainder of this note I use definitions 1 only. There is a technical difference between cardinal and ordinal numbers. The distinction can be seen in the way that these numbers are used. A number used to designate the size of a seti.e., to answer the question, "How many?"is used cardinally. Any use that depends on the position of the number in the prescribed sequence is the ordinal use of the number. The number found at the top or bottom of a page in a book is an example of the ordinal use of the number. "set theory", Encyclopædia Britannica Online
  • 12. German Grammar: Cardinal Numbers & Ordinal Numbers - Grammatik Der Deutschen Spr
    A comprehensive guide to German grammar A list of german numbers, both cardinal and Ordinal, with explanations of each and a comparison with English
    http://www.vistawide.com/german/grammar/german_numbers.htm
    German
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    German numbers List of cardinal and ordinal numbers About cardinal numbers About ordinal numbers ... GRAMMAR INDEX The numbers in German are cognates of their English equivalents. Like in English, the German numbers are based on a decimal system. In addition, German has both cardinal and ordinal numbers, as English does. Cardinal numbers are the numerals you use to count: one, two, three

    13. Russian Cardinal Ordinal Numbers
    Russian Vocabulary cardinal and Ordinal numbers with English translation.
    http://learnrussianfree.com/vocabulary/numbers-english-russian.aspx
    Learn Russian Free .com
    Books, software, dictionaries and more Most used Russian Cardinal and Ordinal Numbers with English translation. Back to Russian Vocabulary Words: Select dictionary (at the right) and click on any Russian or English word for more comprehensive definition or translation. Dictionaries for Russian words Dictionary: Multitran -!!Best!! Dictionary: Rambler Reference: Russian Gramota Articles: Accoona Search: Yandex Search: Rambler Dictionaries for English words Dictionary: Multitran Reference: AllWords Reference: Cambridge Reference: Dictionary.com Reference: Infoplease Reference: Merriam-Webster Reference: Onelook Reference: Wikipedia Reference: WordNet Reference: Ultralingua Usage Russian Part-of-speech English Usage Russian Part-of-speech English (card) one (card) two (ord) first (card) three (ord) second (card) five (card) one thousand (card) both (card) four (ord) third (card) ten (card) twenty (card) hundred (card) two (card) forty (card) six (card) thirty (card) much; lots of (card) seven (card) million (card) three; threesome (ord) fourth (card) several (card) eight (card) fifty (ord) fifth (card) one and half (card) fifteen (card) twelve (card) nine Learning Russian as a foreign language.

    14. Hawaiian Cardinal And Ordinal Numbers - UniLang Wiki
    cardinal numbers 19 are preceded by the numeral classifying prefixes ‘e- and ‘a-. However, nowadays the numeral classifier ‘e- is more common.
    http://home.unilang.org/wiki3/index.php/Hawaiian_cardinal_and_ordinal_numbers
    Hawaiian cardinal and ordinal numbers
    From UniLang Wiki
    Contents
    edit
    Cardinal Numbers
    • Cardinal numbers 1-9 are preceded by the numeral classifying prefixes ‘e- and ‘a-. However, nowadays the numeral classifier ‘e- is more common.
    English numbers 0-9 Hawaiian numbers without the numeral classifiers ‘e- and ‘a- Hawaiian numbers with the numeral classifier ‘e- Hawaiian numbers with the numeral classifier ‘a- Zero ‘Ole Does not take the classifying prefix Does not take the classifying prefix One Kahi ‘Ekahi ‘Akahi Two Lua ‘Elua ‘Alua Three Kolu ‘Ekolu ‘Akolu Four Hā ‘Ehā ‘Ahā Five Lima ‘Elima ‘Alima Six Ono ‘Eono ‘Aono Seven Hiku ‘Ehiku ‘Ahiku Eight Walu ‘Ewalu ‘Awalu Nine Iwa ‘Eiwa ‘Aiwa
    edit
    Notes on cardinal numbers 1-9
    1) When counting in a series, it is acceptable to use the numerals 1-9 with our without the numeral classifiers ‘e- and ‘a-. 2) The numeral classifiers ‘e- and ‘a- are used only with the numerals 1-9, and with the numeral interogative -hia thereby produciong ‘ehia and ‘ahia , meaning "How many?" The number and numbers above 9 are not preceded by the numeral classifiers ‘e- and ‘a-.

    15. Spanish Numbers, Cardinal And Ordinal.
    We offer courses in many languages including Spanish, in this page you will learn Spanish numbers, cardinal and Ordinal. and you can also go to the main
    http://vegasociety.com/spanish/numbers.html
    Home Phrases Numbers Articles ... Save this as your homepage! Spanish Numbers Check out this Brain Games site
    This lesson will help you understand the numbers in Spanish (cardinal and ordinal numbers), and enables you to use real examples shown below. If you have any question let us know by clicking on the “Contact us” button, this lesson is very important since it covers a very widely used element in Spanish which is the numerals. Cardinal Numbers in Spanish Cardinal numbers (cardinales) are the numbers used for counting; of course they look the same in Spanish as well as in English: Spanish Numbers cero
    1 uno/a
    2 dos
    3 tres
    4 cuatro
    5 cinco
    6 seis
    7 siete
    8 ocho
    9 nueve 10 diez 11 once 12 doce 13 trece 14 catorce 15 quince 16 dieciséis 17 diecisiete 18 dieciocho 19 diecinueve In Spanish uno becomes un when used in front of a masculine noun : un perro, veintiún perros. To refer to a feminine noun una is used: una mujer, treinta y una mujeres. Uno is used only when counting (uno, dos, tres) or for numerals refering to a masculine noun but does not precede that noun: ¿Cuántos hijos tienes? - Uno (or else we simply write) - un hijo

    16. Ordinal Knowledge: Number Names And Number Concepts In Chinese And English | Can
    Children s understanding of the difference between Ordinal and cardinal numbers is difficult to assess, and the results of a single task should be taken
    http://findarticles.com/p/articles/mi_qa3690/is_200006/ai_n8902623/pg_9
    @import url(/css/us/pub_page_article.css); @import url(/css/us/template_503.css); @import url(/css/us/tabs_503.css); @import url(/css/us/fa_bnet.css); @import url(http://i.bnet.com/css/fa.css); BNET Research Center Find 10 Million Articles BNET.com Advanced Search Find in free and premium articles free articles only premium articles only this publication Arts Autos Business Health News Reference Sports Technology
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    Ordinal knowledge: Number names and number concepts in Chinese and English
    Canadian Journal of Experimental Psychology Jun 2000 by Kevin Miller Susan M Major Hua Shu Houcan Zhang ... < Page 1 Continued from page 8. Previous Next
    Chinese-speaking children face a much simpler inductive task in learning a very straightforward system of ordinal number names. Thus they have fewer opportunities to invent reasonable but incorrect ordinal number names than their English-speaking peers. The structure of number names continues to affect the way in which children learn ordinal numbers well into elementary school. But the difficulty that English-speaking children have in learning larger ordinal number names did not mean that they were at a disadvantage on all tasks involving ordinal concepts. Despite the problems that they had generating larger number names, English-speaking second- and fourth-graders performed well on tasks involving applying showed ordinal numbers to objects, and performed better on tasks involving conceptual understanding of the special properties of ordinal numbers.

    17. The Syntax Of Numbers And Number Words 1. The External Syntax Of
    Each is constructed out of number words. A number word alone (properly inflected) can be a cardinal or Ordinal number, but not a fraction.
    http://lexsrv3.nlm.nih.gov/LexSysGroup/Projects/numbers/current/release/NUMBERS/
    0. A cardinal number of rank N (N>0) consists of a magnitude word of power N preceded by a cardinal number of rank <1 and optionally followed by a cardinal number of rank

    18. English Grammar: DETERMINERS: QUANTIFIERS - NUMBERS ORDINAL AND CARDINAL
    DETERMINERS QUANTIFIERS numbers Ordinal and cardinal, English Language Tools for Grammar, Writing, Punctuation, Pronunciation.
    http://www.english4today.com/englishgrammar/grammar/Determiners10.cfm
    English today.com :: Online English Grammar Home Page Search Blog: Grammar Tips Top Grammar Questions ... Z
    THE QUANTIFIERS
    NUMBERS The cardinal numbers (one, two, three, etc.) are adjectives referring to quantity, and the ordinal numbers (first, second, third, etc.) refer to distribution. Number Cardinal Ordinal one first two second three third four fourth five fifth six sixth seven seventh eight eighth nine ninth ten tenth eleven eleventh twelve twelfth thirteen thirteenth fourteen fourteenth fifteen fifteenth sixteen sixteenth seventeen seventeenth eighteen eighteenth nineteen nineteenth twenty twentieth twenty-one twenty-first twenty-two twenty-second twenty-three twenty-third twenty-four twenty-fourth twenty-five twenty-fifth twenty-six twenty-sixth twenty-seven twenty-seventh twenty-eight twenty-eighth twenty-nine twenty-ninth thirty thirtieth thirty-one thirty-first forty fortieth fifty fiftieth sixty sixtieth seventy seventieth eighty eightieth ninety ninetieth one hundred hundredth five hundred five hundredth one thousand thousandth one hundred thousand hundred thousandth one million millionth Examples:
    • There are twenty-five people in the room.

    19. ORDINAL NUMBERS -BUSINESS SPANISH TUTORIALS
    Ordinal numbers are adjectives used to organize persons and things into a In Spanish, cardinal numbers (arabic numberals) are used for dates except for
    http://www.businessspanish.com/LECCION/ordinals.htm

    20. Cardinal Numbers — Infoplease.com
    cardinal, Ordinal, and Nominal numbers cardinal, Ordinal, and Nominal numbers cardinal numbers, known as the “counting .
    http://www.infoplease.com/dictionary/brewers/cardinal-numbers.html
    Site Map FAQ
    in All Infoplease Almanacs Biographies Dictionary Encyclopedia Spelling Checker
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    Dec 24, 2007
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    21. 3.2 - Ordinal Numbers
    Ordinal numbers FROM 11th ONWARDS. From 11th onwards, you only need to add suffix esimo, and to drop the cardinal number s last vowel (except
    http://www.geocities.com/f_pollett/i-3-2.htm
    ORDINAL NUMBERS
    As suggested by their name, ordinal numbers (1st, 2nd, 3rd... etc.) are used for indicating orders or ranks.
    In Italian, they have specific forms from 1 to 10, while all the following ones use one same suffix, so they are quite easy to learn.
    Unlike cardinal numbers, though, ordinals behave like an adjective, therefore they can have both a masculine and a feminine gender, in both singular and plural forms (all of them are regular).
    Also in this page English sounds are shown.
    ORDINAL NUMBERS FROM 1st TO 9th
    primo pryh moh first secondo seh kohn doh second terzo tehr tzo third quarto quahr toh fourth quinto quihn toh fifth sesto sehs toh sixth settimo seh' ttymoh seventh ottavo oh' ttah voh eighth nono noh noh ninth decimo deh chimoh tenth
    As found in most Western languages, the expressions first and second are irregular (i.e. they have no phonetic relation with their cardinal numbers one and two ), in all the others the name of the digit is still recognizable, though slightly changed:
    tre - ter zo quattro - quar to cinque - quin to , and so on, while many suffixes change.

    22. ScienceDirect - European Journal Of Operational Research : Integration Of Ordina
    In this way the Ordinal numbers Sij and Si j are translated into the stochastic cardinal numbers Image and Image . Then Image and Image
    http://linkinghub.elsevier.com/retrieve/pii/S0377221703004867
    Athens/Institution Login Not Registered? User Name: Password: Remember me on this computer Forgotten password? Home Browse My Settings ... Help Quick Search Title, abstract, keywords Author e.g. j s smith Journal/book title Volume Issue Page European Journal of Operational Research
    Volume 158, Issue 2
    , 16 October 2004, Pages 317-338
    Methodological Foundations of Multi-Criteria Decision Making
    Abstract
    Full Text + Links PDF (401 K) Related Articles in ScienceDirect Ordinal regression revisited: Multiple criteria ranking...
    European Journal of Operational Research

    Ordinal regression revisited: Multiple criteria ranking using a set of additive value functions
    European Journal of Operational Research In Press, Corrected Proof Available online 27 August 2007
    Abstract
    We present a new method, called UTA GMS , for multiple criteria ranking of alternatives from set A using a set of additive value functions which result from an ordinal regression. The preference information provided by the decision maker is a set of pairwise comparisons on a subset of alternatives A R A , called reference alternatives. The preference model built via ordinal regression is the set of all additive value functions compatible with the preference information. Using this model, one can define two relations in the set

    23. Ordinals And Cardinals
    Ordinals and cardinals form the backbone of mathematics. Ordinal numbers describe orderings. cardinal numbers are the measure of size in mathematics.
    http://www.mtnmath.com/book/node54.html
    New version of this book
    Next: Recursive functions Up: Set theory Previous: The axioms of
    Ordinals and cardinals
    Ordinals and cardinals form the backbone of mathematics. Ordinal numbers describe orderings. Cardinal numbers are the measure of size in mathematics. They first ordinals are the integers. , the set containing all integers, is the ordinal of the integers. The next ordinal is the successor of . This set has one members just as the successor of has one set, the set containing the empty set. The successor of is the set containing and the successor of Ordinals can be thought of as general way of representing induction or iteration. corresponds to iteration that can be characterized by a loop up to any integer or induction on all the integers. contains and all finite successors to contains all finite successors to contains for all integers n corresponds to two nest loops each with a limit of any integer. corresponds to loops on the integers nested n deep. corresponds to loops on the integers nested n deep where n is a parameter. All forms of iterations and all induction can be characterized by some ordinal number. By using infinite sets to describe iteration one masks over the rich combinatorial structures that are required to define higher levels of iteration. Recursive iteration is characterized by the recursive ordinals but there is no recursive algorithm to describe the structure of all recursive ordinal

    24. Czech Numbers - Cardinal, Ordinal
    Please let us know if you have trouble downloading and playing the sound files. cardinal numbers Real Audio pronunciation of numbers 1 20
    http://www.locallingo.com/czech/grammar/numbers.html
    A site that helps you learn Czech. home chat links about us ... contact grammar Search this site:
    Visit our sister site at
    myczechrepublic.com Czech Numbers All Czech words are recorded in Real Audio. You can download Real Player by clicking on the icon to the right. Please let us know if you have trouble downloading and playing the sound files. Cardinal Numbers
    Real Audio pronunciation of numbers 1 - 20
    zero nula .wav one jeden / jedna / jedno .wav two dva / dvì .wav three tøi .wav four ètyøi .wav five pìt .wav six ¹est .wav seven sedm .wav - pronounced "sedum" eight osm .wav - pronounced "osum" nine devìt .wav ten deset .wav eleven jedenáct .wav twelve dvanáct .wav thirteen tøináct .wav fourteen ètrnáct .wav fifteen patnáct .wav sixteen ¹estnáct .wav seventeen sedmnáct .wav - pronounced "sedumnáct" eighteen osmnáct .wav - pronounced "osumnáct"

    25. Arabic Numbers, Cardinal And Ordinal
    Our website Speak7 helps you learn Arabic numbers, cardinal numbers, Ordinal numbers in Arabic, and more about Arabic grammar, vocabulary, and expressions
    http://arabic.speak7.com/arabic_numbers.htm
    Home Phrases Calligraphy Translation ... More
    Arabic Numbers
    Salim 2006 © I Like this Page Tell a Friend about this Page Save as Homepage You will learn in this lesson: Arabic numbers, cardinal numbers, ordinal numbers in Arabic. The table below shows examples of Arabic numbers . The first and the fifth columns have numbers used in some Arab countries; they’re not of Arabic origins but still used in many places especially copies of the Holy Qur’an …. Nowadays what we call the Arabic numbers are the numbers shown on the columns 2 and 6, which are used by the Arab world as well as the rest of the world. Arabic Numbers sifr wahid ithnan thalatha (th as in bath) arba’a khamsa sitta sab’a thamaniya (th in th in) tis’a ‘ashra ahada ‘ashar ithna ‘ashar thalatha ‘ashar arba’a ‘ashar khamsa ‘ashar sitta ‘ashar sab’a ‘ashar thamaniya ‘ashar tis’a ‘ashar ‘ishrun wahed wa-’ishrun ithnane wa-’ishrun thalatha wa-’ishrun arba’a wa-’ishrun khamsa wa-’ishrun sitta wa-’ishrun sab’a wa-’ishrun thamaniya wa-’ishrun tis’a wa-’ishrun thalathun wahid wa-thalathun arba’un ithnan wa-arba’un khamsun thalatha wa-khamsun sittun arba'a wa-sittun sab’un khamsa wa-sab’un thamanun sitta wa-thamanun tis’un sab'a wa-tis’un mi'a alf mi'at alf alfain Million Forming numbers in Arabic is quite easy, from 13 to 19 you just place a

    26. Russian Cardinal Numbers
    Numerals (numbers) designate quantity or order in counting. They are divided into Ordinal, collective, fractional and cardinal numbers.
    http://www.masterrussian.com/aa050601a.shtml
    The starting place to learn the Russian language on the Internet. About us Home User agreement Link to Us Subjects Lessons Bookstore Dictionaries Forum ... Video new Pronunciation Reading Translation Verbs ... Software
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    Cardinal Numbers
    Numerals (numbers) designate quantity or order in counting. They are divided into ordinal, collective, fractional and cardinal numbers. Cardinal numbers designate the number of people or things, and answer the question (How many/much?). For example, äâàäöàòü ïÿòü êàðàíäàøåé - 25 pencils Related Resources Ordinal Numerals
    Declension of Adjectives
    External Links Categories of Numerals
    Declension of Numerals
    The good news is that Russian cardinal numbers only change by cases and do not have gender (except ) or number (except The numeral agrees with the related noun by gender, number and case, as in:

    27. Italian Cultural Institute In New Delhi
    Verbs present, present perfect (with to have and to be), future and conditional; articles definite, indefinite; Ordinal and cardinal numbers;
    http://www.iicnewdelhi.esteri.it/IIC_NewDelhi/Menu/Imparare_Italiano/I_corsi_di_
    @import url( ../style/BOXMODEL.CSS ); italiano News The Institute Events ... Courses for foreigners in Italy Level 1 Four-month course 1A General Information  Lenght of course:  99 hours
    Starts:  14 January
    Ends:  14 May
    Calendar:  Monday, Tuesday, Wednesday, Thursday
    Timetable:
    Lenght of lessons:  90 minutes Enrolment  Period of enrolment:  15 December - 13 January
    Qualifications required to apply:  none
    Entrance test:
    Fare of application:  4,000 INR + 1,000 INR for textbooks
    Method of payment:  cash
    Discounts:  for the staff of the Italian Cultural Institute and the Italian Embassy Text-books and teaching-aids  Textbook:  M.Mezzadri, P.Balboni, Rete 1 , Guerra Edizioni Price of the teching-aids:  1,000 INR Teacher, room and number of students  Teachers:  Sonya Gosh, Nina Saxena, Giorgia Cantele Room: Number of students:  from 10 to 25 Syllabus  Description of the course  Functions:  To greet and to introduce oneself; to express what one likes or dislikes; to ask information; to offer something; to thank; to refuse; to explain a problem; to talk about everyday habits; to go shopping; to tell the time; to talk about the weather; to ask and to invite informally and informally; to express possession; to talk about actions in progress; to ask for advice; to talk about quantities; to ask for directions; to express possibilities; to express opinions; to make predictions; to advise; to make suppositions; to compare. Grammatical aspects: Verbs: present, present perfect (with to have and to be), future and conditional; articles: definite, indefinite; ordinal and cardinal numbers; simple and articulated prepositions; plural of nouns; possessive adjectives and pronouns; the verb to like; a few irregular verbs; reflexive verbs; the verb to do; imperative;to be +ing; to want and to have to; demonstrative adjectives; direct pronouns; partitive; there is/there are; all types of comparative; absolute and relative superlative; imperfect; interrogative pronouns and adjectives.

    28. E-Intro To Old English - 9. Numerals
    cardinal numbers 9.3. Ordinal numbers 9.4. Online exercise numbers are of two kinds, cardinal and Ordinal. cardinal numbers (such as Modern English one
    http://www.wmich.edu/medieval/resources/IOE/inflnumb.html
    @import "oeg.print.css"; S kip navigation To p ... . On-line exercise
    Numerals
    9.1. Quick Start
    Numbers are of two kinds, cardinal and ordinal . Cardinal numbers (such as Modern English one two . . .) may function either as nouns or as adjectives: As noun: Fēower sÄ«°on seofon bēo° eahta and twentiÄ¡ Four times seven are twenty-eight As adjective: On ānum d¦Ä¡e bēo° fēower and twentiÄ¡ tÄ«da [In one day there are twenty-four hours] Ordinal numbers (such as Modern English first second . . .) are always adjectives, and all of them are declined weak except for ō°er 'second', which is always strong žone forman d¦Ä¡ hÄ«e hēton Sunnand¦Ä¡ [They called the first day Sunday] žone ō°erne d¦Ä¡ hÄ«e hēton Mōnand¦Ä¡ [They called the second day Monday]
    9.2. Cardinal numbers
    Here are the cardinal numbers one-twelve: ān fēower seofon tÄ«en twēġen, twā fÄ«f eahta endleofan ¾rÄ«e, ¾rēo siex nigon twelf The cardinal ān is usually declined as a strong adjective; when it is declined weak ( āna ) it means 'alone': hē āna l¦Ä¡ 'he lay alone'. The cardinals two and three have their own peculiar inflectional system, shown in table 9.1.

    29. CARDINAL-ORDINAL DIGITAL CALCULATORS AND COMPUTERS - Patent 3718810
    A further object of this invention is to provide a cardinalOrdinal calculator which will operate with both cardinal and Ordinal numbers for providing
    http://www.freepatentsonline.com/3718810.html
    Login or Create Free Account Search Go to Advanced Search Home Search Patents Data Services ... Help Title: CARDINAL-ORDINAL DIGITAL CALCULATORS AND COMPUTERS Document Type and Number: United States Patent 3718810 Link to this page: http://www.freepatentsonline.com/3718810.html Abstract: Application Number: Filing Date: Publication Date: View Patent Images: Images are available in PDF form when logged in. To view PDFs, Login or Create Account (Free!) Referenced by: View patents that cite this patent Export Citation: Click for automatic bibliography generation Assignee: CARDINAL ORDINAL CORP
    Primary Class: Other Classes: International Classes: Field of Search: US Patent References: November 1967 Kitz et al. Primary Examiner: Morrison, Malcolm A. Assistant Examiner: Gottman, James F. Claims: I claim
    1. In a calculator comprising an input keyboard unit having first and second terminals, a central processing unit having first and second input terminals and first and second output terminals, and an output display unit having first and second terminals wherein a cardinal calculator would be formed with the input keyboard unit first terminal being connected to the central processing unit input first terminal, with the central processing unit output first terminal being connected to the output display unit first terminal, with the input keyboard unit second terminal being connected to the central processing unit input second terminal, and with the central processing unit output second terminal being connected to the output display unit second terminal, the calculator comprising an ordinal calculator with

    30. Chapter XI. Definition Of Cardinal Numbers
    Cantor has shown that it is necessary to separate the study of cardinal and Ordinal numbers, which are distinct entities, of which the former are simpler,
    http://fair-use.org/bertrand-russell/the-principles-of-mathematics/chapter-xi
    The Principles of Mathematics
    Chapter XI. Definition of Cardinal Numbers Part II. Number
    Chapter XI. Definition of Cardinal Numbers
    Table of Contents
  • § 107. Plan of Part II § 108. Mathematical meaning of definition § 109. Definitions of numbers by abstraction § 110. Objections to this definition ...
  • n. Cantor has shown that it is necessary to separate the study of Cardinal and Ordinal numbers, which are distinct entities, of which the former are simpler, but of which both are essential to ordinary Mathematics. On Ordinal numbers, cf. Chaps. XXIX XXXVIII infra n. See Peano, F. 1901, p. 6 ff. and Padoa, Th©orie Alg©brique des Nombres Entiers, Congr¨s , Vol. III, p. 314 ff. n. Cf. Burali-Forti, Sur les diff©rentes d©finitions du nombre r©el, Congr¨s , III, p. 294 ff. n. Cf. Peano, F. 1901, § 32, ·0, Note. n. On the necessity of this condition, cf. Padoa, loc. cit. , p. 324. Padoa appears not to perceive, however, that all definitions define the single individual of a class; when what is defined is a class, this must be the only term of some class of classes. Part II. Number 

    31. Minor Categories
    cardinal numbers are tagged NS. Cases where an Ordinal might be expected but without overt Ordinal marking are treated as cardinal numbers and tagged NUM.
    http://www.ling.upenn.edu/hist-corpora/annotation/pos-misc.htm
    Minor categories

    32. WebWorkbooks | Spanish Grammar
    English and Spanish both have cardinal and Ordinal numbers. . express Ordinal numbers above tenth, the cardinal numbers are usually
    http://www.webworkbooks.com/spanish/grammar/numbers.php
    Spanish Grammar Report an error Send to a friend Print page
    Introduction ... Nouns Pronouns
    Verbs
    Adjectives
    Ser and Estar Por and Para ... Comparisons

    Where you are: Spanish Grammar
    Numbers Defined
    Cardinal Numbers Table of Cardinal Numbers ... Table of Fractions
    Numbers Defined Cardinal Numbers Cardinal numbers, or simply cardinals, are those numbers ( one, two, three, four , etc.) that are used to indicate the quantity of things in a group or set. The cardinal numbers answer the question How much ? or How many I have owned four cars. (cardinal) Ordinal Numbers Ordinal numbers, or simply ordinals, are those numbers ( etc.) that indicate the order or position of something in a group or set. The ordinal numbers answer the question Which one ? English and Spanish both have cardinal and ordinal numbers. This is the fourth car I have owned. (ordinal) top
    CARDINAL NUMBERS
    Uno and ciento and its multiples are the only cardinal numbers that change form.

    33. Discovery Channel's Cosmeo
    Ordinal vs. cardinal numbers, cardinal numbers are counting numbers (one, two, three,…) and Ordinal numbers indicate the position of things in a set (first,
    http://www.cosmeo.com/viewwebmath_topic.cfm?guidcatid=2b987a6e-fc74-4424-b8f8-94

    34. Best Coding Practices - Outputing Ordinal Numbers In ASP
    Every language has Ordinal and cardinal numbers. cardinal numbers are the ones we do math with. Ordinal numbers answer the question Which One? .
    http://www.bestcodingpractices.com/outputing_ordinal_numbers_in_asp-20.html
    Currently online: member(s), 10 guest(s)
    ASP Best Practices
    Outputing Ordinal Numbers in ASP Converting regular numbers to Ordinal numbers, as in 1st, 2nd, 3rd and so on.
    Author : Travis Hawkins / Date : 2006-04-04
    Average members rating : Every language has ordinal and cardinal numbers. Cardinal numbers are the ones we do math with. Ordinal numbers answer the question "Which One?". For instance "Which beer was your favorite?", "The 12th one.". Twelfth, or 12th is an ordinal number. It is much more "real world" than computers usually get. Converting numbers to ordinal for the purpose of displaying, especially in the case of dates, can go a long way to make a site look professional. We always say it's the "little things" that make greatness. Well, this is one of the little things. It's not difficult to do, it just takes a minute but it can make a big difference. So here is how to convert am english number into ordinal.
    Code: Function intToOrdinal(i)
    sNum = cStr(i)
    iNum = i mod 10
    select case iNum
    case 1
    sExt = "st"

    35. Greek Sans Flexions - Numbers
    1 Ordinal and cardinal numbers; 2 Writing numbers with letters; 3 Decimals; 4 Fractions Ordinal and cardinal numbers. The basic Ordinal and numbers are
    http://gsf.wunschzetel.de/numbers
    Numbers in Greek sans flexions
    Table of Contents
    (skip table of contents)
    Ordinal and cardinal numbers
    The basic ordinal and numbers are: Numbers in Greek sans flexions number
    in digits number
    in letters cardinal number ordinal number
    Note: the forms in are old words indicating “ x times”, e.g. “three times; thrice”; “five times”. The full series of such numbers will not be explained here, as they are used only in very large cardinal numbers and in ordinals greater than two thousand. (The GSF way to indicate “ x times” is with the noun “once, twice, five times”.)
    Writing numbers with letters
    Numbers can be written with Arabic digits as in English (e.g. “2007” for “two thousand and seven”), or they can be written with letters, similar to the system used in Hebrew and Ancient Greek. The thirty-five letters of the basic alphabet (without the four additional letters ) are used to represent the numbers from one to nine; ten to ninety; a hundred to nine hundred; and a thousand to eight thousand. The letter omega ( )—not otherwise used in GSF—is used to represent the number nine thousand.

    36. Ordinal Number - Wikipedia, The Free Encyclopedia
    In this case, it is traditional to identify the cardinal number with its initial Ordinal, and we say that the initial Ordinal is a cardinal.
    http://en.wikipedia.org/wiki/Ordinal_number
    var wgNotice = ""; var wgNoticeLocal = ""; var wgNoticeLang = "en"; var wgNoticeProject = "wikipedia";
    Ordinal number
    From Wikipedia, the free encyclopedia
    Jump to: navigation search This article is about the mathematical concept. For ordinals in linguistics, see Ordinal number (linguistics) In set theory ordinal ordinal number , and transfinite ordinal number refer to a type of number introduced by Georg Cantor in to accommodate infinite sequences and to classify sets with certain kinds of order structures on them. Ordinals are an extension of the natural numbers different from integers and from cardinals Well-ordering is total ordering with transfinite induction , where transfinite induction extends mathematical induction beyond the finite. Ordinals represent equivalence classes of well orderings with order-isomorphism being the equivalence relationship. Each ordinal is taken to be the set of smaller ordinals. Ordinals may be categorized as: zero, successor ordinals, and limit ordinals (of various cofinalities ). Given a class of ordinals, one can identify the α-th member of that class, i.e. one can index (count) them. A class is closed and unbounded if its indexing function is continuous and never stops. One can define addition, multiplication, and exponentiation on ordinals, but not subtraction or division. The Cantor normal form is a standardized way of writing down ordinals. There is a many to one association from ordinals to cardinals. Larger and larger ordinals can be defined, but they become more and more difficult to describe. Any ordinal number can be made into a

    37. English Numbers
    English numbers. Explanations cardinal numbers Ordinal numbers Phonetic Transcription of English numbers; Specifics Phone numbers The Figure 0
    http://www.ego4u.com/en/cram-up/vocabulary/numbers
    setFontsize(''); Skip menu the fun way to learn English /* Font '); /*]]>*/ Search: auf Deutsch ENG/GER Dictionary Webster
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    38. Cardinal Number -- From Wolfram MathWorld
    (This is not true for the Ordinal numbers.) In fact, the cardinal numbers are obtained by collecting all Ordinal numbers which are obtainable by counting a
    http://mathworld.wolfram.com/CardinalNumber.html
    Search Site Algebra
    Applied Mathematics

    Calculus and Analysis
    ... Religious Terminology
    Cardinal Number In common usage, a cardinal number is a number used in counting (a counting number ), such as 1, 2, 3, .... In formal set theory , a cardinal number (also called "the cardinality") is a type of number defined in such a way that any method of counting sets using it gives the same result. (This is not true for the ordinal numbers .) In fact, the cardinal numbers are obtained by collecting all ordinal numbers which are obtainable by counting a given set. A set has aleph-0 ) members if it can be put into a one-to-one correspondence with the finite ordinal numbers . The cardinality of a set is also frequently referred to as the "power" of a set (Moore 1982, Dauben 1990, Suppes 1972). In Georg Cantor's original notation, the symbol for a set annotated with a single overbar indicated stripped of any structure besides order, hence it represented the order type of the set. A double overbar then indicated stripping the order from the set and thus indicated the cardinal number of the set. However, in modern notation, the symbol is used to denote the cardinal number of set.

    39. Math Forum - Ask Dr. Math
    The definition given in the book tells us that cardinal numbers tell how many (12 shirts per box), Ordinal numbers tell position or order (1st place,
    http://mathforum.org/library/drmath/view/56998.html

    Associated Topics
    Dr. Math Home Search Dr. Math
    Numbers: Cardinal, Ordinal, Nominal?
    Date: 10/25/1999 at 07:55:36 From: Mr. Tomlinson Subject: Math My math class is learning about cardinal, ordinal, and nominal numbers. The definition given in the book tells us that cardinal numbers tell how many (12 shirts per box), ordinal numbers tell position or order (1st place, 5th in line) and nominal numbers name things (number on a jersey, a telephone number). So far so good? That's what we thought until we were asked to determine which group of numbers "time" would fit into. We've had a lively discussion here at the International School in Brussels and are hoping that you can help clarify our dilemma. Respectfully, Mr. Tomlinson Date: 10/25/1999 at 08:13:48 From: Doctor Jerry Subject: Re: Math Hello Mr. Tomlinson, Well, time would be like numbers used in measuring length, area, volume, mass, or other physical or geometric quantities. 16 seconds, 12.5 centimeters, 1344.5 cubic meters. I'm a mathematician but I've never heard of nominal numbers nor felt the need of a name. Cardinals or ordinals are familiar and useful. What would pi be? It's just a real number, no other designation needed (except for some purposes one wants to know that pi is not an "algebraic number" but is a "transcendental" number). I think about the set R of real numbers as a given object. We can use them with attached units to measure something or we can associate them with points on a line or we can form them into pairs to model the Euclidean plane or into triples to model Euclidean three space or ... Sorry that I wasn't able to give a crisp, direct answer. - Doctor Jerry, The Math Forum

    40. Counting Of Numbers - Ordinal & Cardinal
    The definitive guide Counting Of numbers for Teach Yourself Hausa Language.
    http://www.teachyourselfhausa.com/counting-of-numbers.php
    var srl33t_id = '3124'; Teach Yourself Hausa.com home Link to Us Contact Us Table Of Contents Hausa Alphabet learn all the alphabet Counting of Numbers Hausa numbers counting Different Type Of Greetings Ways to greet in hausa Asking about Members of the Family About family members Reception How is the party? Farewell Good bye Making Inquiry And Request with why? what? which? who? where? how? In The Dining funiture room dining table Different Nouns: Pronouns Personal and Possessive Days Months Years Months of the year, years, Days of the week Hausa Verbs Nothing but verb Telling Of Time what time is it? Simple Sentences and Market Situation market conversations Contact Us what do you think? Useful Links other sites Link to Us please help us! Paddy Power online betting shop. A Money Saving Tips Never pay full price again! Top 10 Web Hosting Site NEW! Compare web hosting companies. Last Updated Last Updated: Tuesday 28th August 2007 @ 07:09am
    ENGLISH HAUSA Zero Sifili One Daya Two Biyu Three Uku Four Hudu Five Biyar Six Shidda Seven Bakwai Eight Takwas Nine Tara Ten Goma Eleven Goma Sha Daya Twelve Goma Sha Biyu Thirteen Goma Sha Uku Fourteen Goma Sha Hudu Fifteen Goma Sha Biyar Sixteen Goma Sha Shidda Seventeen Goma Sha Bakwai Eighteen Goma Sha Takwas Nineteen Goma Sha Tara Tweenty Ashirin Ashirin da Daya Ashirin da Biyu Ashirin da Uku Ashirin da Hudu Ashirin da Biyar Ashirin da Shidda Ashirin da Bakwai Ashirin da Takwas Ashirin da Tara Talatin Talatin da Daya Talatin da Biyu Talatin da Uku Talatin da Hudu

    41. Lingua::EN::Numbers::Ordinate -- Go From Cardinal Number (3) To Ordinal ("3rd")
    LinguaENNumbersOrdinate go from cardinal number (3) to Ordinal ( 3rd ) for giving the Ordinal form of a number, given its cardinal value.
    http://search.cpan.org/perldoc?Lingua::EN::Numbers::Ordinate

    42. The Meaning Of Decimals -- A Complete Course In Arithmetic
    Which numbers are the cardinal numbers? Which numbers are the Ordinal numbers? Which numbers are the decimal units? What is the function of the decimal
    http://www.themathpage.com/arith/decimals.htm
    var sc_project=798906; var sc_partition=6; var sc_security="32e508b6"; S k i l l
    i n
    A R I T H M E T I C Table of Contents Home Introduction Lesson 2
    THE MEANING OF DECIMALS
    In this Lesson, we will answer the following:
  • Which numbers are the cardinal numbers?
  • Which numbers are the ordinal numbers?
  • Which numbers are the decimal units
  • What is the function of the decimal point?
  • Which decimal unit is at each decimal place? Section 2
  • How do we read a decimal? Section 3
  • In our system of numbering, what is the function of 0?
  • Why do 0's written on the right of a decimal not change its value?
  • How do we compare decimals?
    The counting numbers have two forms called cardinal and ordinal
    Which numbers are the cardinal numbers? One, two, three, four, etc.
    The cardinal numbers answer the question How much? or How many?.
    Which numbers are the ordinal numbers? First, second, third, fourth, etc.
    The ordinal numbers answer the question Which one?. Every language has both cardinal and ordinal numbers.
    Parts Here are the multiples of 5: 5, 10, 15, 20, 25, 30, etc.
  • 43. Inducing Ordinal And Cardinal Representations Of The First, Five Natural Numbers
    Abstract, Examines the prediction that the Ordinal property of natural number symbols is more easily learned by preschoolers than the cardinal property of
    http://www.eric.ed.gov/ERICWebPortal/recordDetail?accno=EJ107809

    44. PlanetMath: Cardinal Number
    for every Ordinal number $ X$ which has the same cardinality as $ S$ . cardinal numbers have the property that for every set $ A$
    http://planetmath.org/encyclopedia/Cardinal.html
    (more info) Math for the people, by the people. Encyclopedia Requests Forums Docs ... RSS Login create new user name: pass: forget your password? Main Menu sections Encyclop¦dia
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    Feedback Bug Reports downloads Snapshots PM Book information News Docs Wiki ChangeLog ... About cardinal number (Definition) A cardinal number is an ordinal number with the property that for every ordinal number which has the same cardinality as . Cardinal numbers have the property that for every set , there exists a unique cardinal number having the same number of elements as "cardinal number" is owned by djao full author list view preamble View style: HTML with images page images TeX source See Also: cardinality cardinal arithmetic Other names: cardinal
    Attachments:
    limit cardinal (Definition) by yark cardinal successor (Definition) by yark successor cardinal (Definition) by yark cardinal arithmetic (Topic) by yark cardinality of the continuum (Definition) by yark aleph numbers (Definition) by yark beth numbers (Definition) by yark
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    45. Greek Numerals:
    Greek numerals cardinal numbers followed by Ordinal numbers. (Greek enas to ena ekatommurio). Figures won’t lie, but liars will figure.
    http://www.wordinfo.info/words/index/info/view_unit/2355
    cardinal numbers followed by ordinal numbers (Greek: enas to ena ekatommurio
    Greek numerals: cardinal numbers followed by ordinal numbers
    (Greek: enas to ena ekatommurio
    Figures won’t lie, but liars will figure. —Charles H. Grosvenor
    The following Greek numbers are essentially based on both classical and modern elements
    enas (enas [m.], mia [fem.], ena [n.]): one; protos , first.
    duo : two; duteros , second.
    treis, tria : three; tritos , third.
    tessereis, tessera : four; tetartos , fourth.
    pente : five; pemptos , fifth.
    exi : six; ektos , sixth.
    epta, ephta : seven; ebdomos , seventh.
    okto, ochto : eight; ogdoos , eighth.
    ennea, ennia : nine; enatos , ninth.
    deka, deca : ten; dekatos , tenth.
    endeka : eleven; endekatos , eleventh. dodeka : twelve; dodekatos , twelfth. dekatreis, dekatria : thirteen; dekatos tritos , thirteenth. dekatessereis, dekatessera : fourteen; dekatos tetartos , fourteenth. dekapente : fifteen; dekatos pemptos , fifteenth. dekaexi : sixteen; dekatos ektos , sixteenth. dekaepta, dekaephta : seventeen; dekatos ebdomos , seventeenth. dekaokto, dekaochto : eighteen;

    46. The Ordinal Numbers - Learn Spanish Language
    The Ordinal numbers might be thought of as the adjective form of the cardinal numbers, which are the numbers in the form they are most often used.
    http://spanish.about.com/od/spanishvocabulary/a/ordinal.htm
    zOBT=" Ads" zGCID=" test1" zGCID=" test1 test5" zJs=10 zJs=11 zJs=12 zJs=13 zc(5,'jsc',zJs,9999999,'') z160=zpreC(160,600);z336=zpreC(336,280);z728=zpreC(728,90);z133=zpreC(336,133);zItw=160
    Spanish Language
    var h2=document.getElementsByTagName("h2")[0];if(h2.getElementsByTagName("a")[0].firstChild.nodeValue.length>29)h2.className="long";
  • Home Education Spanish Language
  • Search over 1.4 million articles by over 600 experts Spanish Language About.com Search
    Ordinal Numbers
    h1 = document.getElementById("title").getElementsByTagName("h1")[0];h1.innerHTML = widont(h1.innerHTML);
    In Spanish, They're Seldom Used Above 10
    By Gerald Erichsen , About.com
    More About:
    The ordinal numbers might be thought of as the adjective form of the cardinal numbers, which are the numbers in the form they are most often used. Thus uno ("one") is a cardinal number, while primero ("first") is its ordinal form. (Of course, in Spanish as in English, adjectives often can be used as nouns, so el primero is "the first one.")

    47. Ordinal Numbers
    Ordinal numbers are similar to the numbers that you learned before (they are called cardinal numbers). If ten students ran a race, we would say that the
    http://www.aaamath.com/nam15-ordinals.html
    Ordinal Numbers
    Learn Practice Play Explore ... Next Lesson
    Ordinal Numbers
    When objects are placed in order, we use ordinal numbers to tell their position. Ordinal numbers are similar to the numbers that you learned before (they are called Cardinal numbers). If ten students ran a race, we would say that the student that ran the fastest was in first place, the next student was in second place, and so on. The first ten ordinal numbers are:
    • First Second Third Fourth Fifth Sixth Seventh Eighth Ninth Tenth
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    48. JSTOR What Do Pre-First-Grade Children Know About Number?
    Concepts of equality, cardinal num ber, and Ordinal number are necessary to . The test called cardinal and Ordinal number co-ordinated was designed to
    http://links.jstor.org/sici?sici=0013-5984(196304)63:7<397:WDPCKA>2.0.CO;2-Z

    49. Adjectives
    Unpreceded Attributive Comparative Contributive. Irregular Adjectives. Adjectival Phrases. Adjectival Nouns. Ordinal cardinal numbers
    http://www.cybergerman.addr.com/adj.html
    Preceded by Ein Masculine Feminine Neuter Plural Nominative Accusative Dative Genitive e Hose mit einem weiß en Hemd.
    transl) He is wearing black pants with a white shirt.
    ein (attributive) der (attributive) contributive comparative ... top Preceded by Der Masculine Feminine Neuter Plural Nominative Accusative Dative Genitive e Hose mit dem weiß en Hemd.
    transl) He's wearing the black pants with the white shirt.
    ein (attributive) der (attributive) contributive comparative ... top Unpreceded Masculine Feminine Neuter Plural Nominative Accusative Dative Genitive e Hose mit weiß em Hemd.
    transl) He wore black pants with white shirt.
    ein (attributive) der (attributive) contributive comparative ... top Contributive ::Rules:: Contributive adjectives are pretty simple. They are also known as predicate adjectives, which means they come after the noun, not before it. Because they don't precede a noun, they have no noun endings and remain in their original forms.
    tranl) She is really beautiful!

    50. Learn English Online - Free Beginners Course - Unit 5 - Lesson 22 - Ordinal Numb
    Ordinal numbers such as 21st, 33rd etc are formed by combining a cardinal ten with an Ordinal unit. The y of twenty , thirty , forty , etc. is changed
    http://www.learn-english-online.org/Lesson22/Course/Lesson22.htm
    Learn English Online - free beginner's course
    Unit 5 - Lesson - 22 - Ordinal numbers (1 - 1000)
    Remember It
    You should already be able to count up to 1000 in English. The ordinary "cardinal" numbers were covered in Lessons and
    Learn It
    Ordinal Numbers
    Cardinal numbers express quantity: two (2), thirty-five (35) etc... Ordinal numbers indicate order or rank: first (1st), second (2nd), third (3rd) etc... The definite article " the " normally goes in front of an ordinal number: e.g. "Queen Elizabeth the second." For most ordinal numbers, the ending '- th ' is used, with one or two exceptions for those inevitable irregular numbers:- CARDINAL NUMERAL IN WORDS ORDINAL NUMERAL IN WORDS one st the fir st two nd the seco nd three rd the thi rd five th the fif th nine th the nin th twelve th the twelf th Learn your ordinal numbers (requires Real Player Basic
    Ordinal numbers 1 to 19
    In figures In words Pronounce It the first the second the third the fourth the fifth the sixth the seventh the eighth the ninth the tenth the eleventh the twelfth the thirteenth the fourteenth the fifteenth the sixteenth the seventeenth the eighteenth the nineteenth Ordinal numbers such as 21 st rd etc are formed by combining a CARDINAL ten with an ORDINAL unit.

    51. OrdinalNumbers.com | Ordinal Numbers | Ordinal Numbers | Comparing Numbers | Fre
    Ordinal numbers Comparing numbers French cardinal numbers Conn French Horn Serial numbers French numbers 1 To 100 List Of numbers In French
    http://ordinalnumbers.com/
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    52. Ordinal Month
    IMPORTANT The Ordinal numbers after twenty are formed like the Ordinal numbers from one to ten. That means that the cardinal number, 21 (twenty-one),
    http://esl.lbcc.cc.ca.us/eesllessons/month/ordinalmonth.htm
    LBCC E-ESL Online Learning
    Cardinal Numbers, Ordinal Numbers, and the Months and Seasons
    Cardinal Numbers Ordinal Numbers Test Your Knowledge
    Cardinal Numbers
    Cardinal numbers are numbers used for counting things. These are zero, one, two, three, four, and so on. Cardinal numbers are used to describe how many of something there are. For example, there are forty-two (42) computers in the Multimedia Classroom.
    Ordinal Numbers
    Ordinal numbers are numbers used to tell position or order. These are first, second, third, fourth, and so on. Ordinal numbers are usually used to describe what position something has. For example, February is the second month of the year. Ordinal numbers are also used to give dates. May 23, 2000 is pronounced May twenty-third, two thousand. The cardinal numbers from zero to twenty-four are listed below. IMPORTANT The ordinal numbers after twenty are formed like the ordinal numbers from one to ten. That means that the cardinal number, 21 (twenty-one), becomes the ordinal number 21st (twenty-first). Twenty-two becomes twenty-second and twenty-three becomes twenty-third. Twenty-four becomes the ordinal number, twenty-fourth. Similarly, thirty-one, 31, becomes thirty-first and so on.
    Cardinal Number Written Form Ordinal Number Written Form zero zeroth one first two second three third four fourth five fifth six sixth seven seventh eight eighth nine ninth ten tenth eleven eleventh twelve twelfth thirteen thirteenth fourteen fourteenth fifteen fifteenth sixteen sixteenth seventeen

    53. Cardinal Number - Wiktionary
    cardinal numbers may be used as Ordinal numbers when preceded by a singular (countable) noun, especially if preceded by the word number
    http://en.wiktionary.org/wiki/cardinal_number
    var wgNotice = ""; var wgNoticeLocal = ""; var wgNoticeLang = "en"; var wgNoticeProject = "wiktionary";
    cardinal number
    From Wiktionary
    Jump to: navigation search Wikipedia has an article on: Cardinal number Wikipedia
    Contents

    54. Springer Online Reference Works
    Thus, the scale of cardinal numbers is a subscale of the scale of Ordinal numbers. A number of properties of Ordinal numbers carry over to cardinal numbers;
    http://eom.springer.de/c/c020370.htm

    Encyclopaedia of Mathematics
    C
    Article referred from
    Article refers to
    Cardinal number,
    transfinite number , power in the sense of Cantor, cardinality of a set That property of the set which is intrinsic to any set with the same cardinality as . In this connection, two sets and are said to have the same cardinality (or to be equivalent ) if there is a one-to-one onto function with domain of definition and set of values G. Cantor defined the cardinal number of a set as that property of it which remains after abstracting the qualitative nature of its elements and their ordering. By way of stressing the double act of abstraction, Cantor introduced the symbol to denote the cardinal number of . The most commonly used from among the various notations for a cardinal number are the symbols and . If is a finite set containing elements, then . If denotes the set of natural numbers, then (see Aleph ). If denotes the set of real numbers, then , the power of the continuum. The set of all subsets of is not equivalent to or to any subset of Cantor's theorem ). In particular, no two of the sets

    55. Back To Zentralblatt MATH Pages
    Review Small Greek letters denote Ordinal numbers, small Roman letters denote cardinal numbers (i.e. initial Ordinal), always p,r,s \omega0,
    http://www.zblmath.fiz-karlsruhe.de/MATH/general/erdos/cit/15826603.htm
    Back to Zentralblatt MATH Pages
    CD-ROM published
    on the occasion of the
    ICM 1998 in Berlin
    Zentralblatt MATH
    Zbl.No:
    Autor:
    Title:
    Partition relations for cardinal numbers (In English)
    Source: Acta Math. Acad. Sci. Hung. 16, 93-196 (1965).
    Review: Small Greek letters denote ordinal numbers, small Roman letters denote cardinal numbers (i.e. initial ordinal), always is the cardinality of X [X] r denotes the set of all r element subsets of X . The partition relations I, II, III are defined as follows. The relation I: r holds true if and only if for every partition [X] r J a , there is a and a subset such that b and [Y] r . The relation II: means that for every partition [X] J , where [X] [X] r , there exista a and a subset b and [Y] . The relation III: s
    b r ,...,r s p a p X p are disjoint, [X ,...,X s r ,...r s s p r p for J . Then there exist sets Y r r , for and a such that r b for and [Y ,...,Y s r ,...,r s "In this paper our first major aim is to discuss as completely as possible the relation I. Our most general results in this direction are stated in Theorems I and II, ... . If we disregard cases when among the given cardinals there occur inaccessible numbers greater than , and if we assume the General Continuum Hypothesis, then our results are complete for r = ... . It seems that there are only two essentially different methods for obtaining positive partition formulae: those given in Lemma 1 and those given in Lemma 3 ... In Lemma 5 we state powerful new methods for constructing examples of particular partitions which yield negative I-relation. ... Our second major aim is an investigation of the polarized partition relation III."

    56. Recognizing Cardinal Numbers
    Recognizing cardinal numbers Beverly Clayton Walt Disney Magnet School 2611 West 80th Place 4140 We will then change the names from Ordinal to cardinal.
    http://www.iit.edu/~smile/pl9502.html
    Recognizing Cardinal Numbers Beverly Clayton Walt Disney Magnet School 2611 West 80th Place 4140 North Marine Drive Chicago IL 60652 Chicago IL 60613 (312) 778-7318 (312) 534-5846 Objective : To teach students ordinal numbers and their proper places for numerals 1-10. Materials Needed : -scissors -matching sheets -crayons -glue -number signs for 1-10 Strategy Performance Assessment : Each activity has its own built-in assessment. The last activity will show that the objective has been met if the puzzle has been completed. Return to Physics Index

    57. Mises Blog
    cardinal numbers are not a representation of Ordinal rank they are a “representation” plus a quantitative difference between the rankings.
    http://blog.mises.org/archives/002102.asp
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      June 10, 2004
      Value, Utility, and Price (lecture 3 of 34)
      David J. Heinrich
      I'm at the Mises University now, and I plan on transcribing my notes. This is the third lecture given. Any errors are mine, feel free to point them out so that I can correct them. This lecture was given by Prof. Herbener. Basic points about Human Action
      • Human Action, the Action Axiom : man acts, using means to obtain ends, so as to ease unrest felt.
      • The Action Axiom is true in the Aristotlean sense in that nay attempts to disprove it are in fact actions, and are thus self-contradictory.
      • Understanding ( ”verstehen” ) of human action comes from our reflection on conceptual structure.
      • Only human beings as individuals can act; this rules out collective action; thus, we can forgo “group valuation”.
      • How do we reconcile different individuals with the overall group?
      • Appraisal choice between two alternatives, scarcity; in fact, action implies scarcity.
      • Choice is two-dimensional: one thing is chosen , while the next-best thing is forgone

      Choice and Preference
      • Choice is choosing between two alternatives.

    58. Ordinal Number (mathematics) -- Britannica Online Encyclopedia
    The axiom schema of replacement has played a significant role in developing a theory of Ordinal numbers. In contrast to cardinal numbers, which serve to
    http://www.britannica.com/eb/topic-431471/ordinal-number
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    ordinal number (mathematics)
    A selection of articles discussing this topic.
    definition
    The axiom schema of replacement has played a significant role in developing a theory of ordinal numbers. In contrast to cardinal numbers, which serve to designate the size of a set, ordinal numbers are used to determine positions within a prescribed well-ordered sequence. Under an approach conceived by von Neumann, if A is a set, the successor A of A is the set...
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    59. Reference: Understanding Dates & Numbers In Spanish Records - Tarver-Gen: Tarver
    Although English uses Ordinal numbers, such as the tenth of July or July 10th, in Spanish the cardinal numbers are almost always used for the days of the
    http://www.tarver-genealogy.net/aids/spanish/sp_dates_num.html
    You are here: Home Reference Spanish Jump to a feature
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    queries guestbook contact me ... search Site Map / Help Search this site Research Aids Records Reference Visual history Obituaries Cemeteries Memorials GEDCOMs Cirilo data Cockerham data Lee data Matthews data Rogers data Tarver lines Welch data Queries Guestbook Mailing list Genealogy links Fun Stuff Carroll Tarver page Adina Tarver Cirilo Eleazar Cirilo pages
    Spanish-English Translations Dates are usually written out in Spanish records. . [ On the twenty-two day of January in the year of our Lord one thousand eight hundred fifty eight. ] For this reason, an understanding of basic terms associated with dates and numbers will be extremely helpful when tracing your ancestors in Spanish records. The lists on this are designed to help with comprehension of dates as they are recorded in genealogical sources. For a sample translation of a document in which the understanding of dates was imperative, see the [ baptismal record of Jose Daniel Alfrido ] , my second great-grandfather. The

    60. Cardinal - Definition Of Cardinal By The Free Online Dictionary, Thesaurus And E
    2. cardinal being or denoting a numerical quantity but not order; cardinal numbers . Ordinal - being or denoting a numerical order in a series; Ordinal
    http://www.thefreedictionary.com/cardinal
    Domain='thefreedictionary.com' word='cardinal' Printer Friendly 728,498,693 visitors served. TheFreeDictionary Google Word / Article Starts with Ends with Text subscription: Dictionary/
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    Also found in: Medical Acronyms Encyclopedia Wikipedia ... Hutchinson 0.03 sec. car·di·nal (kär dn- l, kärd n l) adj. Of foremost importance; paramount: a cardinal rule; cardinal sins. Dark to deep or vivid red. n. Abbr. Card. Roman Catholic Church A high church official, ranking just below the pope, who has been appointed by a pope to membership in the College of Cardinals. A dark to deep or vivid red. A North American finch (Cardinalis cardinalis) having a crested head, a short thick bill, and bright red plumage in the male. A short hooded cloak, originally of scarlet cloth, worn by women in the 18th century. A cardinal number. [Middle English, from Late Latin cardin lis principal, pivotal , from Latin, serving as a hinge , from card , cardin- hinge car di·nal·ship n.

    61. Cardinal Or Ordinal Numbers In Legal English? (Linguistics)
    Discussion among translators, entitled cardinal or Ordinal numbers in legal English?. Forum name Linguistics.
    http://www.proz.com/topic/60081
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    62. ATrpms - By Distribution > Fedora 7 > Perl-Lingua-EN-Numbers-Ordinate
    perlLingua-EN-numbers-Ordinate-0.01-3.fc7.noarch.rpm - Go from cardinal number (3) to Ordinal ( 3rd ). There are two kinds of numbers in English
    http://atrpms.net/dist/f7/perl-Lingua-EN-Numbers-Ordinate/
    perl-Lingua-EN-Numbers-Ordinate ATrpms by Distribution Fedora 7 Go from cardinal number (3) to ordinal (3rd). Files
    Jun 03 07:44:28 CEST 2007 perl-Lingua-EN-Numbers-Ordinate-0.01-3.fc7.noarch.rpm - Go from cardinal number (3) to ordinal ("3rd"). There are two kinds of numbers in English cardinals (1, 2, 3...),
    and ordinals (1st, 2nd, 3rd...). ... [more]
    Apr 27 11:02:48 CEST 2007 perl-Lingua-EN-Numbers-Ordinate-0.01-3.fc6.93.noarch.rpm - Go from cardinal number (3) to ordinal ("3rd"). There are two kinds of numbers in English cardinals (1, 2, 3...),
    and ordinals (1st, 2nd, 3rd...). ... [more]
    Aug 15 08:59:24 CEST 2006 perl-Lingua-EN-Numbers-Ordinate-0.01-3.src.rpm - Go from cardinal number (3) to ordinal ("3rd"). There are two kinds of numbers in English cardinals (1, 2, 3...),
    and ordinals (1st, 2nd, 3rd...). ... [more]
    Jul 16 18:08:22 CEST 2006 perl-Lingua-EN-Numbers-Ordinate.spec - Go from cardinal number (3) to ordinal ("3rd"). There are two kinds of numbers in English cardinals (1, 2, 3...),
    and ordinals (1st, 2nd, 3rd...).

    63. Debian -- Package Search Results -- Liblingua
    Package liblinguaen-numbers-ordinate-perl. sarge (oldstable) (perl) Perl module to convert from cardinal numbers to Ordinal numbers
    http://packages.debian.org/search?keywords=liblingua&suite=all

    64. Cardinal Number - History
    In linguistics, cardinal numbers is the name given to number words that are used for quantity (one, two, three), as opposed to Ordinal numbers,
    http://www.experiencefestival.com/cardinal_number_-_history
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    Cardinal number, Cardinal number - Cardinal arithmetic, Cardinal number - Formal definition, Cardinal number - History, Cardinal number - Motivation, Cardinal number - The continuum hypothesis, large cardinal, Nominal number, Ordinal number, Serial number, The paradox of the greatest cardinal
    ARTICLES RELATED TO Cardinal number - History
    Cardinal number - History: Encyclopedia - Cardinal number In linguistics, cardinal numbers is the name given to number words that are used for quantity (one, two, three), as opposed to ordinal numbers, words that are used for order (first, second, third). See names of numbers in English. In mathematics, cardinal numbers, or cardinals for short, are a generalized kind of number used to denote the size of a set. While for finite sets the size is given by a natural number, the number of elements, cardinal numbers (cardinality ...

    65. CJR : Resources : Language Corner
    cardinal/Ordinal numbers. cardinal Rules. By Evan Jenkins. A Little League team s players, the article said, picked up their third World Series victory in
    http://www.cjr.org/resources/lc/cardinal.php
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    66. Abstract Set Theory
    set represents an Ordinal that is not denumerable. Strictly speaking the with indices to denote the cardinal numbers of wellordered sets. The cardi
    http://www.questia.com/PM.qst?a=o&docId=77282156

    67. Ordinal Number, Cardinal Number. The Columbia Guide To Standard American English
    Ordinal number, cardinal number. The Columbia Guide to Standard American English. 1993.
    http://www.bartleby.com/68/21/4321.html
    Select Search All Bartleby.com All Reference Columbia Encyclopedia World History Encyclopedia Cultural Literacy World Factbook Columbia Gazetteer American Heritage Coll. Dictionary Roget's Thesauri Roget's II: Thesaurus Roget's Int'l Thesaurus Quotations Bartlett's Quotations Columbia Quotations Simpson's Quotations Respectfully Quoted English Usage Modern Usage American English Fowler's King's English Strunk's Style Mencken's Language Cambridge History The King James Bible Oxford Shakespeare Gray's Anatomy Farmer's Cookbook Post's Etiquette Bulfinch's Mythology Frazer's Golden Bough All Verse Anthologies Dickinson, E. Eliot, T.S. Frost, R. Hopkins, G.M. Keats, J. Lawrence, D.H. Masters, E.L. Sandburg, C. Sassoon, S. Whitman, W. Wordsworth, W. Yeats, W.B. All Nonfiction Harvard Classics American Essays Einstein's Relativity Grant, U.S. Roosevelt, T. Wells's History Presidential Inaugurals All Fiction Shelf of Fiction Ghost Stories Short Stories Shaw, G.B. Stein, G. Stevenson, R.L. Wells, H.G. Reference Usage The Columbia Guide to Standard American English PREVIOUS ... BIBLIOGRAPHIC RECORD Kenneth G. Wilson The Columbia Guide to Standard American English.

    68. WikiAnswers - Is Fifth An Ordinal Or A Cardinal Number
    15 Is fifth an Ordinal or a cardinal number? Fifth an Ordinal or cardinal number? Is 5 an Ordinal or a cardinal number? Is 5th a ordanal or a cardinal
    http://wiki.answers.com/Q/Is_fifth_an_ordinal_or_a_cardinal_number
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    69. Ordinal Number
    An Ordinal number is one which is used to indicate where in an ordered list someone or something occurs. A number used to tell how many is a cardinal
    http://science.jrank.org/pages/4887/Ordinal-Number.html
    Other Free Encyclopedias Science Encyclopedia Science Encyclopedia Vol 4
    Ordinal Number
    cardinal number one thousand becomes the ordinal number one thousandth; four becomes fourth; and so on. In the case of 1, 2, and 3, however completely different names are used. time The ordinal name of a number is used in some instances where no ranking is intended or where the ranking is vestigial. The names given to the denominators of common fraction are ordinal names although they signify the number of uniform parts into which each unit is cut. Thus three-fifths indicates that each unit has been divided into five equal parts, and the fraction represents three of them. However, when the fraction is written with numerals, 3/5, both numerator and denominator are written in the cardinal form. On the other hand there are times when the cardinal form of a number is used in an ordinal sense. In counting TABLE 1. ORDINAL NUMBERS Cardinal Ordinal Ordinal symbol one first two second 2nd or 2d three third 3rd or 3d four fourth twenty twentieth twenty-one twenty-first one hundred one hundredth one hundred one one hundred first a group of objects one is putting them into one-to-one correspondence infinity have extended the concept of ordinal number to apply to certain classes of infinite numbers as well.

    70. Aeclectic Tarot Forum - Ordinal Vs Cardinal Value
    The alphabetic system was used for Ordinal as well as cardinal numerals, It is their cardinal valuethe value of the glyph considered as a number.
    http://www.tarotforum.net/archive/index.php/t-27261.html
    Aeclectic Tarot Forum PDA View Full Version : Ordinal vs Cardinal value jmd Of interest in Kabalah is whether what may be of greater relevance is a letter's ordinal (first, second, ..., tenth, eleventh, etc) or cardinal (1, 2, 3, ..., 10, 20, etc) value.
    This has special sinificance if one considers some of the Kabalistic claims and counterclaims which have been made for Hebrew-Atouts correlations - irrespective as to whether Alef is to be associated with the Bateleur/Magician, the World, or the Fool.
    For myself, in terms of Atouts/Hebrew letter correlations, I consider the ordinal value of greater importance - after all, the twelfth letter has a (cardinal) value of thirty, and there are not thirty Atouts (nor thirty letters, for that matter).
    If the ordinal value is considered of greater merit, this does not of course show that there exists an intrinsic connection between the Hebrew letters and the Atouts, but rather that comments against correlations based on cardinal value are irrelevent. Ravenswing It's my belief that both of these are of equal importance. The manner in which I look at the glyphs depends on what I am relating them to.

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