Abstract
Cantor defined the cardinal number of a set M to be “the general concept which, by means of our active faculty of thought, arises from the set M when we make abstraction of the nature of its various elements m and of the order in which they are given.” He denoted this cardinal number by \( \overline{\overline M} \). The two bars indicate the two levels of abstraction needed to produce the cardinal number from M. With only one level of abstraction, that is, by only abstracting of the nature of its various elements, we obtain the ordinal number \( \overline M \). Cantor’s definition of cardinal number is clearly not an operational one. Indeed Cantor’s words suggest that cardinal numbers are psychological entities rather than mathematical objects.
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