h2g2 The Hitchhiker's Guide to the Galaxy: Earth Edition

Firstly, I'd like to compliment you on a very nice article. =)
I have a suggestion, though: under each type of proof, state references to other entries where that type of proof is used. For example, Cantor's Diagonal Argument is a great example of proof by contradiction.

Yes, good article.

I would, ideally, add an arithmetic example of proof by induction:

to prove that something is true for all positive integers, there are two
steps: it must be true for 1; and if it is true for n then that must imply it is true for n+1.

So, to prove that the sum of all integers from 1 to n is n(n+1)/2

first step. 1(1+1)/2 =1

second step: for some n the sum is n(n+1)/2

then for n+1 the sum is n(n+1)/2 + (n+1) ; just adding the next number.

n(n+1)/2 +(n+1)
= (n+1)(n/2 +1)
= (n+1)(n/2+ 2/2)
= (n+1)(n+2)/2 ; the formula for n+1