$0^{0}$

Depending on what you need, $0^{0}$ could be many things. Coming from every positive power of 0 ( $0^{1}$ , $0^{2}$ , etc), it must be $0$ . Coming from every negative power of 0 ( $0^{-1}$ , $0^{-2}$ , etc) then it must be $undefined$ . Seeing that, for every other number, the power of zero is 1, $0^{0}$ must be $1$ too. Then what is it?

The thing is, there is no actual equation or complicated sum for this. You just have to change it out of $1$ , $0$ &. $undefined$ to sort your preference. But most of the time it is 1.

#NumberTheory

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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}`	$\boxed{123}$

Comments

That's interesting Praveen. Sounds a lot like $\frac{0}{0}$ . If you use the rule that $0$ divided by anything must equal $0$ , then $\frac{0}{0}=0$ . However, if you use the rule that any number divided by itself is $1$ , then $\frac{0}{0}=1$ . But if you use the rule that anything divided by $0$ is infinity (okay, not really something widely agreed upon, but I happen to think this is the case), than $\frac{0}{0}=\infty$ . Hence why mathematicians say $\frac{0}{0}$ is undefined.

David Stiff - 1 year, 3 months 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}`	$\boxed{123}$

000^{0}00

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$0^{0}$