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4. Formal Logic / F. Set Theory ST / 3. Types of Set / d. Infinite Sets

[sets which contain an infinity of members]

10 ideas
An infinite set maps into its own proper subset [Reck/Price on Dedekind]
Cantor showed that supposed contradictions in infinity were just a lack of clarity [Potter on Cantor]
We can enumerate finite classes, but an intensional definition is needed for infinite classes [Russell]
We understand some statements about all sets [Putnam]
Set theory says that natural numbers are an actual infinity (to accommodate their powerset) [Brown,JR]
Set theory made a closer study of infinity possible [Clegg]
Any set can always generate a larger set - its powerset, of subsets [Clegg]
The continuum is the powerset of the integers, which moves up a level [Clegg]
Those who reject infinite collections also want to reject the Axiom of Choice [Lavine]
Infinite sets correspond one-to-one with a subset [Friend]