Ideas from 'works' by Giuseppe Peano [1890], by Theme Structure

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6. Mathematics / B. Foundations for Mathematics / 3. Axioms for Number / a. Axioms for numbers
Numbers have been defined in terms of 'successors' to the concept of 'zero'
6. Mathematics / B. Foundations for Mathematics / 3. Axioms for Number / d. Peano arithmetic
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)