A Conversation for Basic Methods of Mathematical Proof
Jaz Started conversation Nov 25, 2000
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.
aging jb Posted Jul 19, 2004
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+1)(n/2 +1)
= (n+1)(n/2+ 2/2)
= (n+1)(n+2)/2 ; the formula for n+1
Key: Complain about this post