Resolution Needed: 0^0=?

I've noticed that problems involving $0^{0}$ get a lot of reports and comments debating what the answer is. It seems that Brilliant members are divided into two sides: one saying it is indeterminate, the other saying it is $1$ .

I believe we need to come up with a collective agreement on what the value of $0^{0}$ is so that we avoid future chaos/confusion/conflicts. The purpose of this note is not to decide on the "right answer," but to decide how we can all compromise. What would be the best way to do this?

Please comment your opinion below. Thank you for reading this note!

#Algebra #Exponents #RealNumbers #Brilliant #0

Easy Math Editor

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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

I think it is indeterminate, waiting for the staff to give the opinion!

Swapnil Das - 6 years, 1 month ago

@Calvin Lin Mr. Lin, I would like to ask for your opinion on how this debate can be settled for problems posted on Brilliant in the future. Thank you.

Nadia Jo - 6 years, 1 month ago

I think we need to have a vote, I know some people do not have opinions, but maybe it would be okay for this to be done on a problem by problem basis. If a problem requires the solution of 0 to the 0 and they do not want it to be 1 or indeterminate(whichever we decide to make as the basis) they can state in the problem what the definition of 0 to the 0 is.

Rmflute Shrivastav - 6 years, 1 month ago

Well, many conventions defined $0^{0}$ as $1$ .

William Park - 6 years, 1 month ago

If you search "0^0" in Google, the Google calculator tells me that it's 1. Of course, I can't completely trust Google's answer, but I think it's 1.

William Park - 6 years, 1 month ago

Again, this is NOT intended for discussing what the answer is. This is intended for discussing how we can all agree on an answer.

Nadia Jo - 6 years, 1 month ago

Okay... we should vote!

William Park - 6 years, 1 month ago

Ya!

Swapnil Das - 6 years, 1 month ago

@Swapnil Das – @Calvin Lin Is it possible to have a vote?

William Park - 6 years, 1 month ago

@William Park – I guess, he will allow it!

Swapnil Das - 6 years, 1 month ago

Well, Youtube sources say that it is undefined, including the numberphile. Further, it's proof has also been derived by calculus.

Swapnil Das - 6 years, 1 month ago

I think it should be 1

Jahnvi Verma - 6 years, 1 month ago

Indeterminate. For textbooks that consider real number arithmetic only, it is often convenient to just define 0^0=1 however.

Bejoy Sen - 6 years, 1 month ago

Google says 1... But Wolfram Alpha says indefinite.

Jules Le Menestrel - 6 years, 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}`	$\boxed{123}$