Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

This question already has an answer here:

A friend showed me this proof:

Proof: 2 = 1

$$Let \space x= y$$

Multiply both sides by x:

$$x^2= xy$$

Subtract $y^2$ from both sides:

$$x^2-y^2= xy-y^2$$

Factor:

$$(x+y)(x-y) = y(x-y)$$

Cancel out $(x-y)$ from both sides:

$$(x+y) = y$$

Simplify (Because $x=y$):

$$y+y=y$$

$$2y = y$$

$$2 = 1$$

Where does the logic break down? Everything is done to both sides.

share|improve this question

marked as duplicate by Git Gud, Thomas Andrews, N. S., Aang, Maisam Hedyelloo Jul 17 '13 at 19:24

This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.

5  
Don't divide by $0$. Just...don't do it. –  David Mitra Jul 17 '13 at 19:11
    
$0*1=0*99999 \Rightarrow 1=99999$ for sure –  igf Jul 17 '13 at 19:12
2  
You can't cancel $0$ in the equality $0\cdot1=0\cdot2$ –  Sami Ben Romdhane Jul 17 '13 at 19:13
    
After the factor is done, $(x-y)=0$ thus both sides become zero and this exercise is finished. Dupe of these questions: math.stackexchange.com/questions/417324/… and math.stackexchange.com/questions/117998/… –  JB King Jul 17 '13 at 19:18
2  
This must be a duplicate. –  TMM Jul 17 '13 at 19:18

1 Answer 1

You cannot cancel out the $(x-y)$. You defined $x=y$, so you end up dividing by $0$.

share|improve this answer

Not the answer you're looking for? Browse other questions tagged or ask your own question.