Definitions
from Wiktionary, Creative Commons Attribution/ShareAlike License
 adj. Having equal cardinality.
Etymologies
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Examples

In the first example, we have two concepts that are equinumerous:

The number of Fs is identical to the number of Gs if and only if F and G are equinumerous.

Instead numbers were to be defined as classes of equinumerous classes.

Examples he cited were the Frege/Russell definition of numbers as classes of equinumerous classes, the theory of definite descriptions, the construction of matter from sense data, and several others.

For Bolzano, equipollence and “having exactly the same kind of construction” (die ganz gleiche Entstehungsart haben) are taken together as a sufficient condition for infinite sets being equinumerous or having the same cardinal number.

Crispin Wright's ˜neoFregean™ programme shows how Peano's postulates can be derived within the framework of secondorder logic from nothing except the Humean principle that the same number attaches to equinumerous concepts.

This brings him close to Frege's idea that the number of a given class is the class of all classes equinumerous to that given class.

In this problem, which has historically been presented as concerning "marriage", there are two disjoint equinumerous sets, which we may call "men" and "women".

Oresme's proof is somewhat reminiscent of Georg Cantor's (1845 “ 1918) demonstration that certain infinite sets are equinumerous.

If numbers are supposed to be identical if and only if the concepts they are numbers of are equinumerous, what guarantee do we have that every concept has a number? p253)
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