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# for the clever mathematician

is zero to the power of zero=1 ?
DeWayfarer · 61-69, M
Zero or any defined number, yes!

Now ask: To what is the imaginary number raised to the zero power equal?

[i]i[/i]^⁰ ?

Since [i]i[/i] is undefined, the result can not be defined. 🤷🏻‍♂️

[i]i[/i] is only defined with an even number power.

[i]i[/i]^ⁿ = -1, where n= 2,4,6... ∞

0 by definition is a member of the empty set, so it's neither even nor odd.
DeWayfarer · 61-69, M
@SomeMichGuy [center][big][b][i][c=1F5E00]𝓗𝓪𝓿𝓮 𝓪 𝓰𝓸𝓸𝓭 𝓭𝓪𝔂! 😊[/c][/i][/b][/big][/center]
@DeWayfarer lmao I am. I already helped steer others away from your obvious errors, so that's a definite win, so thanks for that opportunity.
DeWayfarer · 61-69, M
@SomeMichGuy [center][big][b][i][c=1F5E00]𝓗𝓪𝓿𝓮 𝓪 𝓰𝓸𝓸𝓭 𝓭𝓪𝔂! 😊[/c][/i][/b][/big][/center]
Tukudo · 41-45, M
MasterLee · 56-60, M
@Tukudo 😯-😛=6 inches
Tukudo · 41-45, M
@MasterLee did you mean 😯 minus 😛= 6 inches?
MasterLee · 56-60, M
@Tukudo indeed
Alison · 18-21, F
Afaik the jury is still out. Its undefined
espoir · 36-40, F
Alison · 18-21, F
@espoir not when I looked it up, i mighta got more hardcore than you tho🤷‍♀️, I didnt just take the first answer.
Anyways this arguement is as dumb as:
Does nothing exist?
Life is too short
espoir · 36-40, F
@Alison at least it's defined. And it can be used in an equation
CestManan · 46-50, F
I heard that when a mathematician gets constipation, he works it out with a pencil.
@CestManan OUCH!
Pfuzylogic · M
anything to the power of zero is 1.
@Pfuzylogic That quote illustrates some pretty poor reasoning.

Given:

x^p, for p > 0

we know that

x^{-p} = 1/(x^p)

so

(x^p) * (x^{-p}) = (x^p) * [1/(x^p)] = 1

but

(x^p) * (x^{-p}) = x^{p + (-p)} = x^0

So

x^0 = 1, for any positive x

Thus

lim_{x ‐> 0+} x^0 = 1

(since δ^0 = 1 for arbitrarily small δ).
Pfuzylogic · M
@SomeMichGuy
i think your proof would require a post secondary math background. Just keeping it very simple!
@Pfuzylogic The last part--the limit stuff--is from calculus, but the first part is just high school.

Adding exponents (when the base is the same) comes from there, as well as being shown that a number raised to a neg. exponent is just

1/(that number raised to the pos. exponent)

Those two things lead immediately to the general result.

The "limit" thing is also conceptually simple. Since x^0 = 1 is true for even a billionth or a trillionth, etc., it's true for ANY positive number arbitrarily close to 0. So, in the limit as x goes to 0 through positive values, it makes sense that
0^0 = 1.
Northwest · M
Yes, this is the accepted answer that any computer will deliver. However, there have been attempts to make the answer undetermined. I go with 1.
fakable · T
the answer depends on the system in which the question is asked.

if the expression "zero to the power of zero" has a mathematical meaning, then the answer could be number 1.

if the expression has no mathematical meaning, then the answer can be 0, an undefined answer or no answer.
KiwiBird · 36-40, F
Simple. However you may need to define the context of your question otherwise the answer will be undefined.
@KiwiBird Sorry, no.
Tastyfrzz · 61-69, M
Interestingly my calculator says that 0^0 is undefined or 1. I always assumed it was 1.
Guess that answers where the dark matter went.
Yes.
Yes.
auris · M
zero