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# Topic: Ordinal number

 Ordinal number - Wikipedia, the free encyclopedia Ordinals may be categorized as: zero, successor ordinals, and limit ordinals (of various cofinalities). Ordinals may be used to label the elements of any given well-ordered set (the smallest element being labeled 0, the one after that 1, the next one 2, "and so on") and to measure the "length" of the whole set by the least ordinal which is not a label for an element of the set. Any ordinal can be made into a topological space by endowing it with the order topology (since, being well-ordered, an ordinal is in particular totally ordered): in the absence of indication to the contrary, it is always that order topology which is meant when an ordinal is thought of as a topological space. en.wikipedia.org /wiki/Ordinal_number   (4273 words)

 mmtheorems28 - Metamath Proof Explorer The successor of an ordinal number is an ordinal number. The successor of an ordinal number is the smallest larger ordinal number. The union of the ordinal subsets of an ordinal number is that number. metamath.planetmirror.com /mpegif/mmtheorems28.html   (859 words)

 Ordinal number   (Site not responding. Last check: 2007-10-22) Ordinal numbers, or ordinals for short, are numbers used to denote the position in an ordered sequence: first, second, third, fourth, etc. The mathematician Georg Cantor showed in 1897 how to extend this concept beyond the natural numbers to the infinite and how to do arithmetic with these transfinite ordinals. The size aspect leads to cardinal numbers, which were also discovered by Cantor, while the position aspect is generalized by the ordinal numbers described here. There are ordinal numbers which can not be reached from ω with a finite number of the arithmetical operations addition, multiplication and exponentiation. www.teachtime.com /en/wikipedia/o/or/ordinal_number.html   (1190 words)

 Ordinal number Viewed this way, every natural number is a well-ordered set: the set 4 for instance has the elements 0,1,2,3 which are of course ordered as 0<1<2<3 and this is a well-order. A natural number is smaller than another if and only if it is an element of the other. The first transfinite ordinal is ω, the set of all natural numbers. www.ebroadcast.com.au /lookup/encyclopedia/or/Ordinal.html   (1239 words)

 Successor ordinal - Wikipedia, the free encyclopedia When defining the ordinal numbers, an absolutely fundamental operation that we can perform on them is a successor operation S to get the next higher one. An ordinal number which is S(β) for some ordinal β is called a successor ordinal. Ordinals which are neither zero nor successors are called limit ordinals. en.wikipedia.org /wiki/Successor_ordinal   (154 words)

 Ordinal number   (Site not responding. Last check: 2007-10-22) Category:Set theory Ordinal numbers, or ordinals for short, are numbers used to denote the position in an ordered sequence: first, second, third, fourth, etc. (See How to name numbers.) In mathematics, ordinal numbers are an extension of the natural numbers to accommodate infinite sequences, introduced by Georg Cantor in 1897. Arithmetic operations on ordinals can be captured by algorithms that transform Cantor normal forms, similar to, but more complicated than, the algorithms for integer arithmetic in terms of the decimal notation usually taught in primary education. Ordinals which don't have an immediate predecessor can always be written as a limit of a net of other ordinals (but not necessarily as the limit of a sequence, i.e. ordinal-number.kiwiki.homeip.net   (1112 words)

 ordinal number - Wiktionary Ordinal numbers are general construed as adjectives followed by (countable) nouns in singular: Ordinal numbers are generally considered to be ordered from high to low; so that first place is considered highest, and fifth is lower than second. Ordinal numbers corresponding to numbers higher that 20 use cardinal numbers for all the places preceding the final ordinal part: en.wiktionary.org /wiki/ordinal_number   (173 words)

 Ordinal number articles on Encyclopedia.com   (Site not responding. Last check: 2007-10-22) transfinite number TRANSFINITE NUMBER [transfinite number] cardinal or ordinal number designating the magnitude (power) or order of an infinite set ; the theory of transfinite numbers was introduced by Georg Cantor in 1874. number NUMBER [number] entity describing the magnitude or position of a mathematical object or extensions of these concepts. The Natural Numbers Cardinal numbers describe the size of a collection of objects; two such collections have the same (cardinal) number of objects if their members can be matched in www.encyclopedia.com /SearchResults.aspx?Q=Ordinal+number   (147 words)

 RDEGRAAF.nl [Mathematics: Set Theory and Numbers] In formal set theory, an ordinal number (sometimes simply called an "ordinal" for short) is one of the numbers in Georg Cantor's extension of the whole numbers. This is the "smallest" of Cantor's transfinite numbers, defined to be the smallest ordinal number greater than the ordinal number of the whole numbers. In common usage, a cardinal number is a number used in counting (a counting number), such as 1, 2, 3,.... www.rdegraaf.nl /index.asp?sND_ID=915157   (491 words)

 Ordinal number - Simple English Wikipedia Ordinal numbers (or ordinals) are numbers that show something's order, for example: 1st, 2nd, 3rd, 4th, 5th. The yellow shirt is the third one, and the white tee-shirt is the fourth one. The first, second, third, and fourth in this case are ordinal numbers. simple.wikipedia.org /wiki/Ordinal_number   (195 words)

 Creation Passages: "Day" with an Ordinal Number   (Site not responding. Last check: 2007-10-22) An "ordinal" number is distinguished from a "cardinal" number. The ordinal number not only tells you that there are six items, but it tells you that you are referring to the sixth in the sequence. The purpose of this study is to determine whether "day" with an ordinal number refers to an undefined period of time or whether it refers specifically to literal days. www.biblestudylessons.com /cgi-bin/gospel_way/day_with_ordinal.php   (2239 words)

 Ordinal Month Ordinal numbers are numbers used to tell position or order. Ordinal numbers are usually used to describe what position something has. That means that the cardinal number, 21 (twenty-one), becomes the ordinal number 21st (twenty-first). esl.lbcc.cc.ca.us /eesllessons/month/ordinalmonth.htm   (196 words)

 Ordinal knowledge: Number names and number concepts in Chinese and English Canadian Journal of Experimental Psychology ... Ordinal number names are typically learned later than cardinal names, but languages also differ in the regularity with which they form these names. Elementary school children in China and the U.S. showed differences in the acquisition and use of ordinal numbers corresponding to linguistic differences in ordinal names in their native languages. These results suggest that (a) children induce their language's set of ordinal number names by generalization based on rules sanctioned by early examples, and (b) the relation between ordinal names and ordinal concepts is a complex one, with language only one source of difficulty in understanding ordinal relations. www.findarticles.com /p/articles/mi_qa3690/is_200006/ai_n8902623   (431 words)

 Ordinal Numbers The first ten ordinal numbers are : first, second, third, fourth, fifth, sixth, seventh, eighth, ninth, and tenth. She again explains to the class the ordinal numbers show position. Next to the ordinal numbers the students have written on their papers, the students write the name of the object that goes with the number. www.glc.k12.ga.us /BuilderV03/LPTools/LPShared/lpdisplay.asp?LPID=15128   (492 words)

 ordinal number A number used to give the position in an ordered sequence: first, second, third, fourth... Ordinal numbers are distinct from cardinal numbers (one, two, three, four,...), which describe the size of a collection. The mathematician Georg Cantor showed in 1897 how to extend the concept of ordinals beyond the natural numbers to the infinite and how to do arithmetic with the resulting transfinite ordinals (see infinity). www.daviddarling.info /encyclopedia/O/ordinal_number.html   (138 words)

 PlanetMath: ordinal number   (Site not responding. Last check: 2007-10-22) Cross-references: natural numbers, ordinal arithmetic, theory, ordering relation, well ordered set This is version 3 of ordinal number, born on 2002-01-05, modified 2004-03-17. Re: a post for entry "ordinal number" by mathforever planetmath.org /encyclopedia/OrdinalNumber.html   (176 words)

 Ordinal Number   (Site not responding. Last check: 2007-10-22) a number used to indicate place or position within a set or group, ie. An ORDINAL NUMBER is one that shows the ORDER of an item in a sequence. number is used to represent an ordinal number as well as in every case where a cardinal number is used to number a time period, the number is... www.ordinalnumber.info   (335 words)

 Ordinal induction Solving problems in the Arithmetical and Hyperarithmetical hierarchies requires ordinal induction which is a generalization of induction on the integers. The ordinals generalize the integers into the transfinite. Induction on the integers and ordinal induction are compared in Figure 6.1. www.mtnmath.com /whatrh/node52.html   (485 words)

 Ordinal Numbers Ordinal numbers tell the position or order of objects. If ten students ran a race, the student that ran the fastest would be in first place, the next student would be in second place, and then there would be third, fourth, fifth, sixth, seventh, eighth, ninth and tenth places. What is the ordinal number for the last object? www.aaamath.com /B/g23_orx1.htm   (58 words)

 Nominal Number   (Site not responding. Last check: 2007-10-22) Please look for Nominal Number, Example Of A Nominal Number and Ordinal Number to find more Nominal Number information. Nominal numbers are numbers used for identification only. Boundary layer temperature recovery factor on a cone at nominal mach number six. www.nominalnumber.info   (262 words)

 [No title] If the base or power are not numbers or if the power is fractional then an empty string is returned. Gives the ordinal number of a given counting number. This template returns the ordinal number for a given counting number as a word. xsltsl.sourceforge.net /math.html   (155 words)

 MySQL Lists: perl: Re: Ordinal number within a table   (Site not responding. Last check: 2007-10-22) RE: Ordinal number within a table - Kapoor, Nishikant, June 28 2005 4:28pm RE: Ordinal number within a table - Kapoor, Nishikant, June 29 2005 3:14pm RE: Ordinal number within a table - Jamie McCarthy, June 29 2005 8:17pm lists.mysql.com /perl/3569   (178 words)

 Ordinal Numbers   (Site not responding. Last check: 2007-10-22) Please look for Ordinal Numbers, Math, Ordinal Numbers and Ordinal Number Teaching to find more Ordinal Numbers information. Suggested writing exercise: Write ten sentences using all of the ordinal numbers. Type the short form of the ordinal numbers in each of the boxes below. www.ordinalnumbers.info   (203 words)

 ordinal number   (Site not responding. Last check: 2007-10-22) What's the seventh prime number if the primes are ordered from smallest to largest? What's the 5th cube (number which is the cube of a natural number)? Name the 5th place to the left of the decimal. www.mathnstuff.com /math/spoken/here/1words/o/o10.htm   (101 words)

 The Ordinal Number Function - Developer Fusion, the UK developer community - VB, ASP, C#, .NET, PHP and XML tutorials ... The Ordinal Number Function - Developer Fusion, the UK developer community - VB, ASP, C#,.NET, PHP and XML tutorials and source code They simply care for numbers—not ordinals, like “2nd” or “43rd”. Pass it a number and it’ll look up the appropriate suffix through a series of Select routines, and then return the ordinal value. www.developerfusion.co.uk /show/3915   (522 words)

 Ordinal Numbers - Glossary Definition - UsingEnglish.com Home > Reference > Glossary > O > Ordinal Numbers First, second, third, etc., are ordinal numbers, usually coming before a noun. They can be written as 1st, 2nd, 3rd, 4th, etc. www.usingenglish.com /glossary/ordinal-number.html   (67 words)

 Quia - 38 Ordinal Number Match-Up Match the Latin ordinal number to its English counterpart. See a list of terms used in this activity. To learn how to make your own, just like this, click here. www.quia.com /cm/99911.html   (39 words)

 [OpenH323]Duplicate Ordinal number   (Site not responding. Last check: 2007-10-22) Downloaded the latest CVS yesterday and now I get a "duplicate ordinal number - 3268" message when compiling the release version of ptlib. Debug version compiles fine, though Any guess as to why that would be? ..\..\..\Lib\Release\ptlib.def : fatal error LNK1121: duplicate ordinal number "3268" LINK : fatal error LNK1141: failure during build of exports file Error executing link.exe. www.openh323.org /pipermail/openh323/2002-June/022417.html   (234 words)

 Fields() ordinal number - dBforums If you would prefer not to see any double-underlined words and corresponding advertisements, please click here. dBforums > Usenet Groups > comp.databases.* > comp.databases.ms-access > Fields() ordinal number I need to enter data in successive fields of a new record in a recordset using a www.dbforums.com /t841201.html   (551 words)

 The Cats In Line Activity Page Ordinal numbers indicate positions or the order of objects. If ten people ran in a race, the person that ran the fastest would be in first place. Click here for the best bookstore prices on Jan Brett books www.janbrett.com /piggybacks/ordinal.htm   (69 words)

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