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6. Mathematics / A. Nature of Mathematics / 4. The Infinite / f. Uncountable infinities

[infinities beyond the bounds of natural numbers]

5 ideas
Cantor needed Power Set for the reals, but then couldn't count the new collections [Lavine on Cantor]
The naturals won't map onto the reals, so there are different sizes of infinity [George/Velleman on Cantor]
Sets larger than the continuum should be studied in an 'if-then' spirit [Putnam]
Mathematics and science do not require very high orders of infinity [Boolos]
'Aleph-0' is cardinality of the naturals, 'aleph-1' the next cardinal, 'aleph-ω' the ω-th cardinal [Lavine]