Quote: Peano's axioms for number concern 0, unique successors, and induction

Quotation

The three primitive ideas in Peano's arithmetic are: 0, number, successor. By "successor" he means the next number in the natural order. ... (1) 0 is a number (2) The successor of any number is a number. (3) No two numbers have the same successor. (4) 0 is not the successor of any number. (5) Any property which belongs to 0, and also to the successor of every number which has the property, belongs to all numbers. The last of these is the principle of mathematical induction.   Google-1   Google-2

Published before 1923

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