# A Mathematical Proof that Two Equals One

#### 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 $x = y$.

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

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

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

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

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

## One thought on “A Mathematical Proof that Two Equals One”

1. I see the mistake 🙂