Introduction

Since it’s Christmas let us break a leg for a while from learning and thinking about serious mathematical proofs. In this post, I am going to prove something fun — something that is counterintuitive. If you love challenge, think about the proof and justify why it is right or wrong.

In this post, I will prove that two equals one.

Theorem: 2 = 1

Proof

Let $latex x = y$.

Multiply both sides by $latex x$: $latex x^2 = xy$

Add $latex x^2$ to both sides: $latex 2x^2 = x^2 + xy$

Subtract $latex 2xy$ from both sides: $latex 2x^2 – 2xy = x^2 – xy$.

Factor out $latex x^2 – xy$ : $latex 2(x^2 – xy) = 1(x^2-xy)$

Divide both sides by $latex x^2 – xy$: $latex 2 = 1$. $latex \blacksquare$