# Is this logic of solving $\frac{0}{0}$ correct [duplicate]

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I have seen such proofs many times and was unable to prove where it was wrong (not a math person-my bad).
For example the following proof for $\frac{0}{0} = 2$ looks like it is proven correctly - but somehow I feel that it cannot be right.

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This could be pun but I want to know where it is wrong

## marked as duplicate by Matthew Towers, gebruiker, Daniel W. Farlow, Chill2Macht, ShaileshJun 7 '16 at 0:00

• It is wrong when in the beginning ou assume that $\frac 00$ is defined. – Hagen von Eitzen Jun 6 '16 at 18:10
• It involves canceling a $(10-10)$ in middle, which is forbidden, as $(10-10)=0$. – Brian Cheung Jun 6 '16 at 18:11
• It is especially wrong when you divide the top and bottom of the fraction by $0$ – Omnomnomnom Jun 6 '16 at 18:11
• Any argument that uses the expression $\frac{0}{0}$ is wrong. Sometimes a wrong argument happens to yield a correct answer. – André Nicolas Jun 6 '16 at 18:11
• $0 \cdot 4 = 0 \cdot 1 \Rightarrow 4 =1$ by cancelling out the zeros. Which is clearly nonsense. The laws of maths specifically disallow dividing by zero. So no this is not a proof. There are lots of false proofs which rely on hiding a division by zero. – Warren Hill Jun 6 '16 at 18:18

What is wrong is that you can't consider $\frac 00$ in the first place. So everything you will do after that will just be false, because it's from something which is false.
You can show the same way that $\frac 00=3$, and this is nonsense.
Plus, you can't not simplify by $10-10$, because you can never simplify by $0$.