If "one" has a property, and number successors have the property, all numbers have the property {mathematical induction postulate} {induction postulate}. It is a Dedekind-Peano postulate.
Positive-integer axiomatic theory has postulates {Peano's postulates} {Peano postulates} {Dedekind-Peano postulates}. "One" is a number. The number "one" is not any number's successor. A number successor is a number. No two numbers have same successor. If "one" has property and if number successor has property, all numbers have property {induction postulate, Peano}.
3-Mathematics-Axiomatic Theory
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Date Modified: 2022.0225