Combining Texts

All the ideas for 'works', 'The Theory of Transfinite Numbers' and 'works'

expand these ideas     |    start again     |     specify just one area for these texts

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6 ideas

4. Formal Logic / F. Set Theory ST / 1. Set Theory

9616	A set is a collection into a whole of distinct objects of our intuition or thought [Cantor]

4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / a. Axioms for sets

3340	Von Neumann defines each number as the set of all smaller numbers [Neumann, by Blackburn]

4. Formal Logic / F. Set Theory ST / 8. Critique of Set Theory

3355	Von Neumann wanted mathematical functions to replace sets [Neumann, by Benardete,JA]

5. Theory of Logic / D. Assumptions for Logic / 3. Contradiction

10121

Contradiction is not a sign of falsity, nor lack of contradiction a sign of truth [Pascal]

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

22716

Von Neumann defined ordinals as the set of all smaller ordinals [Neumann, by Poundstone]

6. Mathematics / A. Nature of Mathematics / 5. The Infinite / f. Uncountable infinities

15896

Cantor needed Power Set for the reals, but then couldn't count the new collections [Cantor, by Lavine]