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)

1coin

 

2coin

 

 

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 \,

About webmaths

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.
This entry was posted in Teaching Ideas and tagged . Bookmark the permalink.

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.

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