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6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / f. Cardinal numbers

[numbers relating to total rather than position]

8 ideas
A cardinal is an abstraction, from the nature of a set's elements, and from their order [Cantor]
We aren't sure if one cardinal number is always bigger than another [Russell]
To understand finite cardinals, it is necessary and sufficient to understand progressions [Benacerraf, by Wright,C]
A set has k members if it one-one corresponds with the numbers less than or equal to k [Benacerraf]
To explain numbers you must also explain cardinality, the counting of things [Benacerraf]
Aleph-1 is the first ordinal that exceeds aleph-0 [Bostock]
A basic grasp of cardinal numbers needs an understanding of equinumerosity [Heck]
Cardinal numbers answer 'how many?', with the order being irrelevant [Friend]