What's wrong?

\[\begin{align*} \frac{0}{0} &= \frac{100 - 100}{100 - 100} \\ &= \frac{10^2 - 10^2}{10(10 - 10)} \\ &= \frac{(10 + 10)\cancel{(10 - 10)}}{{10\cancel{(10 - 10)}}} \\ &= \frac{20}{10} \\ &= \boxed{2}\end{align*}\]

#NumberTheory

Easy Math Editor

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`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$

Comments

My opinion would be the very first line: equating $\frac{0}{0}$ to anything. It is an undefined expression, so everything which follows must remain undefined.

David Stiff - 1 year, 1 month ago

I think the third step is wrong too, cancelling $0$ by $0$ is not allowed.

Adhiraj Dutta - 1 year, 1 month ago

True!

David Stiff - 1 year, 1 month ago

I agree with @David Stiff.

A Former Brilliant Member - 1 year, 1 month ago

I should also add that the only other truly undefined expression would be $\frac{\infty}{\infty}$ . The value of this expression, as that of $\frac{0}{0}$ can not be successfully derived from any other equation, including $\frac{1}{0} = \infty$ .

David Stiff - 1 year, 1 month ago

I also agree with that, @David Stiff as infinity is limitless.

A Former Brilliant Member - 1 year, 1 month ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$