Results 31 to 40 of about 85 (82)
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The ABC of cardinal and ordinal number representations
Trends in Cognitive Sciences, 2008Numerical cognition encompasses the concepts of quantity ('how many?') and serial order ('which position?'). Yet, although numbers can convey different meanings, a recent imaging study by Fias and coworkers showed that ranking letters in the alphabet is subserved by a cortical network highly similar to that involved in judging magnitudes.
Simon N, Jacob, Andreas, Nieder
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Cardinal Number and Ordinal Number
2010Recall from Chapter 13 that we write card A = card B if there is a bijection A → B. Then we say that A and B have the same cardinal number. We write card A ≤ card B if there is an injection A → B. In this latter case we say that the cardinal number of A is less than or equal to the cardinal number of B. Recall that card N ≤ card R but card N ≠ card R.
Matthias Beck, Ross Geoghegan
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One first? Acquisition of the cardinal and ordinal uses of numbers in preschoolers
Journal of Experimental Child Psychology, 2012We studied the acquisition of the ordinal meaning of number words and examined its development relative to the acquisition of the cardinal meaning. Three groups of 3-, 4-, and 5-year-old children were tested in two tasks requiring the use of number words in both cardinal and ordinal contexts.
Angels, Colomé, Marie-Pascale, Noël
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The theorem of the means for cardinal and ordinal numbers
Mathematical Logic Quarterly, 1993AbstractThe theorem that the arithmetic mean is greater than or equal to the geometric mean is investigated for cardinal and ordinal numbers. It is shown that whereas the theorem of the means can be proved for n pairwise comparable cardinal numbers without the axiom of choice, the inequality a2 + b2 ≥ 2ab is equivalent to the axiom of choice.
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1979
The concept of an ordinal number (or ordinal) was introduced in Section 1.7, where an ordinal was defined to be a woset (X,
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The concept of an ordinal number (or ordinal) was introduced in Section 1.7, where an ordinal was defined to be a woset (X,
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ZDM, 2020
The cardinal and ordinal aspects of number have been widely written about as key constructs that need to be brought together in children’s understanding in order for them to appreciate the idea of numerosity. In this paper, we discuss similarities and differences in the ways in which understandings not only of ordinality, cardinality but also additive ...
Mike Askew, Hamsa Venkat
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The cardinal and ordinal aspects of number have been widely written about as key constructs that need to be brought together in children’s understanding in order for them to appreciate the idea of numerosity. In this paper, we discuss similarities and differences in the ways in which understandings not only of ordinality, cardinality but also additive ...
Mike Askew, Hamsa Venkat
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The Concept of Number: Multiplicity and Succession between Cardinality and Ordinality
South African Journal of Philosophy, 2006No Abstract. South African Journal of Philosophy Vol.
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Real, Cardinal, and Ordinal Numbers
2017A brief development of the construction of the real numbers is given in terms of equivalence classes of Cauchy sequences of rational numbers. This construction is based on the assumption that properties of the rational numbers, including the integers, are known.
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Elementary Counting of Cardinal and Ordinal Numbers by Persons with Mental Retardation
Perceptual and Motor Skills, 1989Cardinal and ordinal counting skills were assessed in 37 mentally retarded adult workers and 42 school children with mental retardation. The major results were the very poor performance of the younger children (essentially at chance beyond the numbers 1 and 2) and the overall marked inferiority in ordinal compared with cardinal counting.
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Type-raising operations on cardinal and ordinal numbers in Quine's “New foundations”
Journal of Symbolic Logic, 1973In this paper we develop certain methods of proof in Quine's set theory NF which have no counterparts elsewhere. These ideas were first used by Specker [5] in his disproof of the Axiom of Choice in NF. They depend on the properties of two related operations, T(n) on cardinal numbers and U(α) on ordinal numbers, which are defined by the equationsfor ...
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