<s>[INST] Can $\frac {100-100}{100-100}=2$? \begin{align*}
\frac{0}{0} &= \frac{100-100}{100-100} \\
&= \frac{10^2-10^2}{10(10-10)} \\
&= \frac{(10+10)(10-10)}{10(10-10)} \\
&= \frac{10+10}{10} \\
&= \frac{20}{10} \\
&= 2
\end{align*}
I know that $0/0$ isn't equal to $2$, the what is wrong in this proof? I wasn't satisfied after searching it on Google, any help would be appreciated.
 [/INST] $1.$ You cannot start with $\frac00$. This is not a number.
$2.$ You are trying to simplify the fraction by dividing numerator and denominator with $(10-10)$. This cannot be done.
Assume beginning from the end going towards the start. The wrong part is when you multiply with $(10-10)$. Because then denominator would be $0.$
With your logic $\frac00=\frac{0*a}{0*b}=\frac{a}b$.
In general: In almost all these kind of problems where someone proves that $1=2$ (or something similar), most of the times, somewhere the denominator will be $0.$
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