A Mathematical Proof that Two Equals One


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


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

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