0^0=0 method

1. Oct 23, 2005

mathelord

a friend [no longer a user of the forum]showed me this and i felt i should as well show this to you all
let x^x=x
x^[1/x]=x
x^[1/x]-x=0
x[x^(1/x-1)-1]=x
so x is 0 and 1.
which evntually gives 0^0 as 0
in sloving with anither method,he also got -1 as x.
how true is the topic 0^0=0.
he explained that if you have nothing and you raise it to nothing you eventually get nothing.

2. Oct 23, 2005

hypermorphism

How did you get from the first step to the second ?

3. Oct 23, 2005

Karlsen

If you have x = 0, you get 1/0 which is invalid.
I also fail to see how you got from the first to the second equation.

4. Oct 23, 2005

roger

I don't actually see how the first equation is valid , never mind the second one.

5. Oct 23, 2005

Karlsen

It's valid because he wants to solve x^x = x, for x.

6. Oct 23, 2005

benjamincarson

mathelord, this is all pretty trivial. What is it that's confusing you? If you "have nothing and you raise it to nothing", then you don't have anything to exponentiate! You don't "eventually" get nothing, it was always nothing.

Last edited: Oct 23, 2005
7. Oct 23, 2005

hypermorphism

Factoring x from 0 and getting x is some pretty nontrivial algebra. :rofl:

8. Oct 23, 2005

benjamincarson

I don't see how he was "factoring x from 0 ". Anyway, It wouldn't be hard to construct a proof that shows that the equation $$x^{x}=x$$ is only valid for 0 and 1. So......
$$0^{0}=0$$
$$1^{1}=1$$

Fiddle-dee-do

9. Oct 23, 2005

Zurtex

Well:

$$\lim_{x \rightarrow 0} x^x = 1$$

$$\lim_{x \rightarrow 0} 0^x = 0$$

Some times 00 = 1 is defined as for usefulness, but in general its not determined.

10. Oct 23, 2005

hypermorphism

Look at his fourth step.
It would be impossible. 00 is an indeterminate form. See here and here.

11. Oct 23, 2005

Robokapp

x^0=1 any number raised to zeor power equals 1. x*x*x*x...*x zeor ammount of times equals 1 because 1 is the null value in multiplication. a number times himself zero times is equal to 1.
0^x=0 zero raised to any power equals zero. 0*0*0*0*0*...0=0 because of multiplication property. no matter how many zeors you have...you still have zero.

0^0=? Well...is it 1 becasue it is raised to zeor parts? or is it 0 becasue the 0 is raised to a power? Can't be both, but it can be none. answer: undefined.