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.

I find this slightly funny. I saw this on a meme:$$\begin{align}a=x\\ a+a=a+x\\ 2a=a+x\\ 2a-2x=a+x-2x\\ 2(a-x)=a+x-2x\\ 2(a-x)=a-x\\ 2=1\end{align}$$ How can these strange algebraic manipulations not be true? I feel that this is a stupid question but it's just weird how people come up with these things. Is there some kind of theorem or something that would make this untrue?

share|improve this question
1  
1  
The problem in many of these false proofs becomes more apparent if you choose numbers for the variables. –  Jair Taylor Dec 6 '12 at 5:35
    
By all these responses I'm feeling kind of dumb... I just thought it was funny that someone actually took the time to do this. –  TheHopefulActuary Dec 6 '12 at 5:54
add comment

4 Answers

up vote 8 down vote accepted

Yes there is:

Theorem: If you divide by $0$ you can prove anything ;)

share|improve this answer
4  
And by Godel, you can't prove everything. Take the contrapositive, and voila! –  Jebruho Dec 6 '12 at 5:33
add comment

you can't devide two side by $(a-x)$, beacuse $a-x=0$.

share|improve this answer
add comment

You first assumed $a=x$ so the line before the last one is $2(a-a)=a-a$.

Indeed $2\cdot 0 = 0$ but you can not deduce $2=1$ from it since you divided by $a-a=0$.

share|improve this answer
add comment

As soon as you get to the fourth step, your equations are all equivalent to $0 = 0$, and you need to be careful about dividing.

share|improve this answer
add comment

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

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