This is laid out here threadbare, and explanations will come if asked for.

Given: This is Mathematicians Village

Suppose: Everyone understands Mathematical Induction

Corollary: If someone doesn't understand, they'll ask 'bout it.

Prove: 1=2

(This has to be done using algebra no more complex than high-school-level.)


Let: x = 1
=> (implies that) x=x
=> x^2 = x^2 (squares of equal amounts)
=> x^2 - x^2 = x^2 - x^2
=> (x^2 - x^2) = (x-x)(x+x) (product of two squares)
=> x(x-x) = (x+x)(x-x) (removing x as a common element from both sides)
=> x = (x+x)
Now lets say x = 1
=> 1 = 1+1
=> 1 = 2

Hence the very foundation of mathematics stands disproved. Anyone care to offer an explanation as to how this is possible?)


Explanations:
(product of two squares)
=> (a-b)(a+b) = a^2 + ab - ab - b^2
=> (a-b)(a+b) = a^2 - b^2