Let's Entertain Karen (July 10)

July 10, 1998

This week's item for the entertainment of Karen is a simple mathematical proof. Don't be alarmed - it doesn't require a calculator or even the ability to do anything other than simple algebra. The easiest way to try and follow it is to write down each step on a piece of paper. I almost guarantee that no-one will figure out why it "works", so here's your big chance to prove me wrong...

How to prove that 1=2

Let a = 1

(multiply both sides by - 1)

- a = - 1

(add a² to both sides)

a² - a = a² - 1

(simplify)

a(a - 1) = (a + 1)(a - 1)

(divide both sides by (a - 1))

a = a + 1

(substitute a = 1)

1 = 1 + 1

(nearly there)

1 = 2

(!!??!!)

How can that be right???

Let a = 1	(multiply both sides by - 1)
- a = - 1	(add a² to both sides)
a² - a = a² - 1	(simplify)
a(a - 1) = (a + 1)(a - 1)	(divide both sides by (a - 1))
a = a + 1	(substitute a = 1)
1 = 1 + 1	(nearly there)
1 = 2	(!!??!!)