Talk:Mathematical induction

Article Checklist for "Mathematical induction"

Workgroup category or categories	Mathematics Workgroup [Categories OK]
Article status	Developing article: beyond a stub, but incomplete
Underlinked article?	Yes
Basic cleanup done?	Yes
Checklist last edited by	--AlekStos 16:18, 24 March 2007 (CDT)

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A simple example of inductive proof

We need a simple example of an inductive proof: something easy to understand, but preferably something that doesn't have an even easier proof without induction. The problem on this web page might be a good example: [1] --Catherine Woodgold 12:04, 6 May 2007 (CDT)

problems

I have some problems with the leading section. Maybe it's my language level and terminology problem, but... consider the following remarks:

• inductive proof is not a proof by cases. The latter describes a reasoning when the statement to be proved is split in a _finite_ number of cases (called also "proof by exhaustion" or brute force in computer science). See famous 4 colors problem.
• is is applicable _whenever_ the problem can be divided into enumerable propositions. IMHO, the image is too simplistic: "divide the problem and you can prove it by induction". Wouldn't it be better to say "it is _used_ to prove an infinite number of statements that have similar form and depend on an integer parameter n" -- or something along these lines.
• modus ponens does not apply... In fact the mathematical induction can be viewed as a far-reaching generalization of this concept, but it is not correct to say "modus ponens is used" (there is infinity in question!)... (BTW, do we need Latin at the beginning?)

Besides, I agree that the chosen example is not the simplest explanation of the idea. So shall we rework all of this? --Aleksander Stos 09:59, 15 May 2007 (CDT)