why is zero raised to zero undefined but every other number raised

pepe

>>8787152
lim a,b ---> 0 a^b = ??????

>>8787152
When working with integers, 0^0 = 1, but when you extend the definition of exponentiation to real numbers the equality doesn't hold anymore because x^y is not continuous in (0, 0)

>>8787181
I don't understand what you're trying to communicate to me friend.

I'm currently working on getting 100% on algebra on khan academy.

>>8787192
Okay, since you haven't had calculus let me put it this way

why is zero raised to zero undefined but zero raised to any other number is zero?

why is zero raised to zero undefined but every other number raised to zero equals 1?


These arguments both use the same logic, but they give contradictory results. Please try again

>>8787223
[math]0^0 = 1 [/math], by definition. i'm not sure what you're asking

>>8787192
Khan has a video on this.

>>8787152
0^3 = 0*0*0
0^2 = 0*0
0^1 = 0
0^0 = 0/0 = undefined.
The whole thing with 0th power isn't just a definition - it means that the number is divided by itself. You can't divide by zero, so naturally you can't raise 0 to the 0th power.

>>8787268
That definition is hardly widely agreed upon.

>>8787309
x^x is formaly defined as Exp(xln(x)) which is not defined at 0 but it does gave a limit which is 1.

>>8787331
But we're not talking about the limit, we're talking about the value at 0, which is not guaranteed to be the same as the limit.

>>8787351
the value at zero is undefined because division by zero is undefined, as >>8787287 said

>>8787287
Can't we take the limit of x^x as x -> 0?

File: 39f65dd90121a42f69cbfd6aaedf7080.png (47KB, 1296x541px) Image search: [Google]

47KB, 1296x541px

>>8787432
No.

>>8787223
^ this is a good attempt at answering the question. look at it again >>8787268 and think.

>>8787223
case 1: [math]0^a=0[/math]
case 2: [math]a^0=1[/math]
how would you choose which one to use if [math]a=0[/math] in the first case or if [math]a=0[/math] in the second case? it is therefore undefined.

have you tried logarithms

>>8787539
>logarithms
doode this is aweeesome

>>8787152
why is zero raised to zero undefined but 0 raised to any other power equals 0?

Who comes up with this shit and why do we listen to them?

>>8787152

Lets say that 1% of earth's population has 90% of all the money.

Why do (they) have 100% power over 99% of the population?

Now let's say I invented a green engine that runs on water air and garbage, and I become so filthy rich that I enter the 1% that has 100% power.

Being a nice guy, I now give a portion of my power over de 99% of the population to people who do not have power.

What is money worth, when all power is divided by those who need it?

0^100%=1/100%
0/99% = 100%-1%

>>8787287
This threads over

>>8787152
because 0 doesnt actually exist.

it can also be thought of in a set theoretic sense.
[math]a^b[/math] represents the number of functions from a set of cardinality [math]a[/math] to a set of cardinality [math]b[/math]. There is only one function from the empty set to the empty set (the empty function), and so by convention [math]0^0 = 1[/math].

although as >>8787309 said the convention depends on the application

>>8787152
Biologists

[eqn]\sum_{n=0}^\infty 0^n = 0^0 + 0^1 +0^2+...= 0^0 + 0 +0+... = 0^0 [/eqn]
By the formula for the geometric series, also
[eqn]\sum_{n=0}^\infty 0^n = \frac{1}{1-0} = 1 [/eqn]