[Math Lair] The Five Peano Postulates

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  1. 1 is a positive integer.
  2. Every positive integer has a unique positive integer as its successor.
  3. No positive integer has 1 as its successor.
  4. Distinct positive integers have different successors.
  5. If a statement holds for the positive integer 1, and if, whenever it holds for a positive integer, it also holds for that integer's successor, then the statement holds for all positive integers.

The fifth postulate is the basis for the principle of mathematical induction.