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Ideas for 'The Evolution of Logic', 'Fath and Love, or the King and Queen' and 'Set Theory and Its Philosophy'

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7 ideas

6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / e. Ordinal numbers

13463

There are at least as many infinite cardinals as transfinite ordinals (because they will map) [Hart,WD]

13492

Von Neumann's ordinals generalise into the transfinite better, because Zermelo's ω is a singleton [Hart,WD]

13459

The less-than relation < well-orders, and partially orders, and totally orders the ordinal numbers [Hart,WD]

13491

The axiom of infinity with separation gives a least limit ordinal ω [Hart,WD]

6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / g. Real numbers

13446

19th century arithmetization of analysis isolated the real numbers from geometry [Hart,WD]

6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / c. Counting procedure

10712

If set theory didn't found mathematics, it is still needed to count infinite sets [Potter]

6. Mathematics / A. Nature of Mathematics / 5. The Infinite / a. The Infinite

13509

We can establish truths about infinite numbers by means of induction [Hart,WD]