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# cardinal number

noun
1.
Also called cardinal numeral. any of the numbers that express amount, as one, two, three, etc. (distinguished from ordinal number).
2.
Also called potency, power. Mathematics. a number or symbol analogous to the number of elements in a finite set, being identical for two sets that can be placed into one-to-one correspondence:
The cardinal number of the set a1, a2, … an is n.
Origin of cardinal number
1585-1595
First recorded in 1585-95
Dictionary.com Unabridged
Based on the Random House Dictionary, © Random House, Inc. 2018.
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Examples from the Web for cardinal number
Historical Examples
• Thus the cardinal number of α is itself a class, and furthermore α is a member of it.

• Thus the cardinal number one is the class of unit classes, the cardinal number two is the class of doublets, and so on.

• The cardinal number zero is the class of classes with no members; but there is only one such class, namely—the null class.

• The relation-number of a relation should be compared with the cardinal number of a class.

• In the above example 2R is an integral real number, which is distinct from a rational integer, and from a cardinal number.

• What business has this cardinal number octiesque uno in a row of ordinals?

John Fiske.
• The Latin language often employed the ordinal number instead of the cardinal number.

Napoleon III, Emperor of the French, 1808-1873.
• The notion of order, which is here introduced, is one which is not required in the theory of cardinal number.

• Two equally numerous collections appear to have something in common: this something is supposed to be their cardinal number.

Bertrand Russell
British Dictionary definitions for cardinal number

## cardinal number

noun
1.
a number denoting quantity but not order in a set Sometimes shortened to cardinal
2.
(maths, logic)
1. a measure of the size of a set that does not take account of the order of its members Compare natural number
2. a particular number having this function
Compare ordinal number
Collins English Dictionary - Complete & Unabridged 2012 Digital Edition
Publishers 1998, 2000, 2003, 2005, 2006, 2007, 2009, 2012
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Word Origin and History for cardinal number
n.

1590s, "one, two, three," etc. as opposed to ordinal numbers "first, second, third," etc.; so called because they are the principal numbers and the ordinals depend on them (see cardinal (adj.)).

Online Etymology Dictionary, © 2010 Douglas Harper
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cardinal number in Science
 cardinal number   (kär'dn-əl)    A number, such as 3, 11, or 412, used in counting to indicate quantity but not order. Compare ordinal number.
The American Heritage® Science Dictionary