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‘Zorn made other contributions to set theory, such as his 1944 paper Idempotency of infinite cardinals in which he proved that an infinite cardinal number is equal to its square.’
‘Defenders of the latter thus resorted to ad boc banishments of such propositions into the realm of meaninglessness; to assert that green is not a cardinal number, they said, is to be guilty of a ‘category mistake.’’
‘Research on the acquisition of cardinal numbers in the two languages will be discussed first, before predictions about the acquisition of ordinal numbers are described.’
‘In Chinese, ordinal names are created by adding a prefix to the cardinal number name.’
‘Three kinds of abilities were assessed: Ability to count with ordinal and cardinal numbers, ability to apply ordinal numbers to objects, and understanding of ordinal concepts.’
‘The ancient Greeks had different systems for cardinal numbers and ordinal numbers so we must look carefully at what we mean by Greek number systems.’
‘Cardinal Algebras presents a study of algebras satisfying certain properties which capture the arithmetic of cardinal numbers.’
‘For finite sets, the cardinal numbers are the whole numbers.’
‘There is a story that it was used as prefix to a number when it was supposed to be read as a cardinal number instead of an ordinal number (#21 = read this as twenty first instead of twenty one).’
‘In 1885 Cantor continued to extend his theory of cardinal numbers and of order types.’
‘Let us consider another simple sort of pattern, small cardinal numbers.’
‘So we see that the word ‘and’ never appears in the written or spoken representations of any cardinal numbers!’
‘Furthermore, ordinal numbers are less frequently encountered than are cardinal numbers.’
‘So far we've only talked about the most basic mathematics - arithmetic and an inbuilt notion of cardinal number.’
‘This pattern of language differences for ordinal numbers is reminiscent of findings for cardinal numbers in a number of ways.’
‘The top panel of Figure 2 presents the median level of abstract counting with cardinal numbers, broken down by age and language.’
‘Quite different properties of cardinal numbers are implied by the poem's stanza, even if qua sonnet its antecedents reach no farther back than Ted Berrigan's fourteen-line accumulations.’
‘I described the U.S. incursion into Cambodia using only the cardinal numbers and the # sign.’
‘The mistakes they make resemble closely the kinds of errors that younger English-speaking children make in the course of mastering the cardinal number names of English.’
‘Mathematics is an area in which one often must master multiple, related symbol systems, such as Arabic numerals and names for ordinal and cardinal numbers.’