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Peano Axioms

Let

If

**N**be the set of natural numbers. Then the properties satisfied by**N**, known as the Peano’s Axioms, are:**Axiom 1: 1 N**, i.e.**1**is a natural number.**Axiom 2:**For each**n N**, there exists a unique natural number**n* N**called the successor of**n**.**Axiom 3: 1 ≠ n*, n N**, i.e.**1**is not the successor of any natural number.**Axiom 4: ∀ m, n N, m* = n* m = n**, i.e. each natural number, if it is a successor, it is the successor of a unique natural number.**Axiom 5:**Principle of finite induction**(P.F.I.)**If

**S ⊂ N**be such that**(i) 1 S**and**(ii) m S m* S**, then**S = N**.**Axiom**

Note:Note:

**1**assures that**N**is not a null set, i.e.**N ≠ Ø**.**Services: -**Peano Axioms Homework | Peano Axioms Homework Help | Peano Axioms Homework Help Services | Live Peano Axioms Homework Help | Peano Axioms Homework Tutors | Online Peano Axioms Homework Help | Peano Axioms Tutors | Online Peano Axioms Tutors | Peano Axioms Homework Services | Peano AxiomsSubmit Your Query ???

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