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

2. Multiply both sides by *a*

3. Subtract

4. Factorise both sides

5. Divide both sides by

6. Observing that

7. Combine like terms on the left side

8. Divide both sides by the non-zero *b*

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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

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