Math Is Fun Forum

{7/3}

Member

Registered: 2013-02-11

Posts: 210

Induction

Hi, I think i have found a way to use induction for integer set too (don't know if it was discovered before this post) by extending the axiom of induction we get "if S is a subset of Z and (a) 0 belongs to S,(b) for n belonging to S (n+1) belongs to S,(c)for n belonging to S (n-1) belongs to S ,then S=Z." if I'm wrong I hope others will correct me.

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anonimnystefy

Real Member

From: Harlan's World

Registered: 2011-05-23

Posts: 16,049

Re: Induction

I think (c) is unneccessary there, and the rest just represents the axiom of induction.

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{7/3}

Member

Registered: 2013-02-11

Posts: 210

Re: Induction

By (c) i stated that -1,-2,-3,-4,... are in S,the general axiom doesn't state that.

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There are 10 kinds of people in the world,people who understand binary and people who don't.

scientia

Member

Registered: 2009-11-13

Posts: 224

Re: Induction

I think (c) is unneccessary there, and the rest just represents the axiom of induction.

It is necessary. This is the induction law for

, not

.

Last edited by scientia (2013-02-17 23:36:12)

{7/3}

Member

Registered: 2013-02-11

Posts: 210

Re: Induction

So,can this axiom be used to prove stuff for integers?

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There are 10 kinds of people in the world,people who understand binary and people who don't.

scientia

Member

Registered: 2009-11-13

Posts: 224

Re: Induction

It looks fine to me. However proving stuff about integers is usually much more straightforward: first prove that the property holds for all non-negative integers, then show that it also holds for

where

is a non-negative integer.