Math Induction (was Re: tabulation of primes)

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Article #657

#657

From: Mark A Biggar
Date: Wed, 12 Aug 1992 21:32

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I have seen two different definitions of induction:

method 1
	prove p(0)
	prove (p(0) & p(1) & ... & p(n)) -> p(n+1)
	therefore p(x) holds for all positive integers

method 2
	prove p(0)
	prove p(n) -> p(n+1)
	therefore p(X) holds etc.

Are these of equal strength, in other words can I prove some things with 1
that I can't prove with just 2?  Which of these is equivalent to the last
peano axiom?

--
Mark Biggar
mab@wdl1.wdl.loral.com

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From: mab@wdl39.wdl.loral.com (Mark A Biggar)
Newsgroups: sci.crypt
Subject: Math Induction (was Re: tabulation of primes)
Message-ID: <1992Aug12.213221.8240@wdl.loral.com>
Date: 12 Aug 92 21:32:21 GMT
References: <1992Aug12.152948.39350@news.th-darmstadt.de> <1992Aug12.171656.8755@tessi.com> <1992Aug12.194603.23527@news.th-darmstadt.de>
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