Why do people think a number to the zeroeth power is 1? It's

>>8695424
>It's clearly fucking zero.
[citation needed]

>>8695424
n to the 0th power is the same as
[math]0/n[/math]

(you)

>>8695424
If x^n/x^m=x^n-m, and n=m, then x^n/x^m=x^0
Since n=m we can have it be
x^n/x^n=x^0
Anything divided by itself is 1, so x^0=1

>>8695424
(n^0) = 1/(n^(-0)) = 1/(n^0) by definition.

Therefore, the only solution is that n^0 = 1, otherwise the previous statement is false.

0^0 is undefined

every other real number to the power of 0 is 1

if you disagree then you're a brainlet

Read this
https://medium.com/i-math/the-zero-power-rule-explained-449b4bd6934d#.5g91ou502

2^2 = 2x2
2^3 = 2x2x2
2^1 = 2
2^0 = 2/2

if you dont understand the pattern you're a retard

>>8696574
And
2^-1 = 2/2/2

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>>8696574

>>8696581
ab^-1 is used more often than any fraction notation in upper math

>>8695424
Because a^0 denotes the identity group element, which under multiplication always means 1.

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>>8696581

ftfy

>>8695424
By definition this is false.
x^0=1 for all x except 0.

More importantly you would break all of mathematics by changing the definition.

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>>8695424

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>>8696561
https://www.google.com/#q=y%3Dx%5Ex

>>8696752
>what are limits?

>>8696756
You want the function to be continous everything else is completly retarded.

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a^n
a=base
n=exponent

The exponent tells you how many times you're going to multiply the base by itself, and then you multiply that by 1.
So for example 2^2=2x2x1 and 2^1=2x1 thus 2^0=1

Genius i know

>>8695424
We have a^{x+y} = a^x a^y and a^{-x} = 1/a^x.

So a^0 = a^{x + (-x)} = a^x a^{-x} = a^x * (1/a^x) = 1. Proof.

>>8696574
It's more like

2^2 = 1x2x2
2^3 = 1x2x2x2
2^1 = 1x2
2^0 = 1
2^-1 = 1/2
2^-2 = 1/2/2

>>8697713
It's more like

2^3 = 1*(2*2*2)
2^2 = 1*(2*2)
2^1 = 1*(2)
2^0 = 1
2^-1 = 1/(2)
2^-2 = 1/(2*2)
2^-3 = 1/(2*2*2)

>>8696935
>being continuous outside its domain

>>8695435
>exponentiation is the same as division
L0Lno fgt pls

>>8696561
>0^0 is undefined
it's defined perfectly well, the problem
is that its value is undecided

>>8695424
Their model of Reality is imperfect.
They believe power is equal to multiplication, because that's what they've been taught.
Some people should spend more time questioning arithmetic (learn to walk before running).

>>8697662
So 2^0 equals no twos times one
Or zero twos times one
Or 0x1=0

>>8695424
no it's not you cunt

>>8696752
It depends on how you approach it
x^x is one way but if you look at other directions (ie complex approach) you get different values
Though I do believe in some applications it is explicitly defined as 1 because it is more useful to treat it that way (I think Knuth proposed this)
Numberphile's problem with zero video has a decent explanation of this issue

What's the lowest possible value of x^x ?

Limit as x approaches 0 for the function f(x) =x^x is 1.

Therefore 0^0=1

Q.E.D.

What is up with fucking brainlets speaking up and thinking their smart, drives me insane.

>>8698655
fuck off, see >>8698545

>>8698655
Lmao this guy is a prime example of how you can sound smart and be a complete fucktard. Parabolic functions within an x/y grid are shit approximations and only morons taught by morons think otherwise.

non-brainlet here. sorry im late. listen dummies this can all be proved with a lil logic and some basic ass 4th grade properties of exponents. when you divide two of the same numbers (thus same base) with the same exponents, take (a^5)/(a^5) for example. when dividing as such youre ultimately just subtracting the exponents from eachother, all the while dividing the same number upon itself, thus being one. therefore, a/a =1, and 5-5=0. sooooooo a^0 = 1. get a piece of paper and write it out if your brain/penis is too small for the mental mathzszsz.

>>8698572
https://www.wolframalpha.com/input/?i=d%2Fdx+(x%5Ex)%3D0

>>8698545
>x^x is one way

It's the best way, the form is the same as 0^0 and the only variable is x.
No side effects.

>>8699002
https://www.google.com/#q=(1%2Fe)^(1%2Fe)

>>8697727
Are you really that retarded?
That concept is 1 semester analysis.

Continuous continuation is a thing you fucking retard.

>>8699541
>analysis
It's calc shit

>>8699558
Its called analysis here in germany.

>>8695512
This

2^2 = 4
2^1 = 2
2^0 =???
2^(-1) = 1/2
2^(-2) = 1/4

Makes sense to me that it would be 1.

>>8695424
I have a thought.. Dunno if its logic is sound..

if
2^2=2*2
2^1=2
2^0=1
2^-1=2/(2)
2^-2=2/(2*2)

and consequently

0^2=0*0
0^1=0
0^0=1
0^-1=0/(0)
0^2=0/(0*0)
,
then in the case of 0^0, the value of 0 changes ? I don't get it...

(Disregarding the fact that one can not divide by 0.. I believe dividing by 0 should result in an infinite value.)

>>8695512
I've always liked this proof so much. I don't even know if you can call it that, but the fact is that it's so cool.

>>8699834
You're wrong twice.
First,
2^-1 =/= 2/2
2^-1 =/= 1/2

Secondly,
>>8696561
> 0^0 is undefined

So there you go.

>>8697791
This is some spicy autism.