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6. Mathematics / A. Nature of Mathematics / 4. The Infinite / i. Cardinal infinity

[infinity as a collection of transcendent size]

5 ideas
You can't get a new transfinite cardinal from an old one just by adding finite numbers to it [Russell]
For every transfinite cardinal there is an infinite collection of transfinite ordinals [Russell]
First-order logic can't discriminate between one infinite cardinal and another [Hodges,W]
Cardinality strictly concerns one-one correspondence, to test infinite sameness of size [Maddy]
Paradox: there is no largest cardinal, but the class of everything seems to be the largest [Lavine]