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Ideas for 'fragments/reports', 'Set Theory and Its Philosophy' and 'works'

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4 ideas

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 / B. Foundations for Mathematics / 4. Axioms for Number / a. Axioms for numbers

3338	Numbers have been defined in terms of 'successors' to the concept of 'zero' [Peano, by Blackburn]

6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / d. Peano arithmetic

5897	0 is a non-successor number, all successors are numbers, successors can't duplicate, if P(n) and P(n+1) then P(all-n) [Peano, by Flew]

17882

It is remarkable that all natural number arithmetic derives from just the Peano Axioms [Potter]