## Can 2 equal 1?

Can you find anything wrong with the following proof that 2 = 1? If not then in our next Maths class I will give you a \$1 coin, and in return you will give me a \$2 coin! (I hope to get rich using Mathematics)

1. Let a and b be equal to non-zero quantities

$a = b \,$

2. Multiply both sides by a

$a^2 = ab \,$

3. Subtract $b^2 \,$

$a^2 - b^2 = ab - b^2 \,$

4. Factorise both sides

$(a - b)(a + b) = b(a - b) \,$

5. Divide both sides by   $(a - b) \,$

$a + b = b \,$

6. Observing that $a = b \,$

$b + b = b \,$

7. Combine like terms on the left side

$2b = b \,$

8. Divide both sides by the non-zero b

$2 = 1 \,$

I have been teaching Mathematics in Victorian secondary schools for 30 years. I use the www to make my maths lessons better. I hope this blog will give other teachers some ideas to try in their own classes.
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### 2 Responses to Can 2 equal 1?

1. mhohrath says:

You are fine until step 5. If a and b are nonzero numbers equal to each other then a – b = 0.
Dividing by zero is undefined

2. Trev says:

I would be checking the author’s ability to factorize if you were seeking the answer to this one.