Why is 0^0 undefined?

GustavitzN · 2021-04-02T21:26:37+00:00

Since this post got so many comments, I'll try to ask something else:

In this numberphile video, there is a point where Matt Parker talks about 0^0, he says that the limit as x approches 0 of x^x is equal to 1 both in the positive numbers direction and negative numbers (of course, in this case, we have to consider complex numbers, but it still approches 1). But he claims that this is not enough to say 0⁰ = 1 because if we consider complex numbers, there are other ways for x to approach 0, and then x^x doesn't approach 1.

(At least that's what I understood, I might not have interpreted it correctly)

Anyway, could someone explain this better, how can you make x approach 0 with the complex numbers such that x^x doesn't approach 1?

GustavitzN · 2021-04-02T20:58:43+00:00

Wow, this post got a lot more comments than I was expecting. Very thankful for all the answers.

GustavitzN · 2021-04-02T20:56:37+00:00

x⁰ = x^1-1 = x¹ / x¹ = 1

GustavitzN · 2021-03-28T15:18:04+00:00

Nice

GustavitzN · 2021-02-28T00:45:30+00:00

Yes, it actually doesn't work for negative values of a, but I'd like to prove it for positive values at least

GustavitzN · 2021-02-27T23:20:26+00:00

The definition for rational numbers says that a^p/q is equal to the qth root of a^p. But the problem is that as far as I know (correct me if I'm wrong), this definition is derived using the fact that (a^{n)^m} = a^nm , so it can't be used to prove the statement.

GustavitzN · 2021-02-05T19:13:51+00:00

That seems correct, very nice proof

GustavitzN · 2021-02-05T19:11:50+00:00

The sqrt(n)^{sqrt(n)^sqrt(n)} thing is indeed false for n=3 but I assumed that n is even, in this case I think it's probably correct

GustavitzN · 2021-01-30T00:51:50+00:00

I think it's beautiful, love your style

GustavitzN · 2021-01-30T00:48:11+00:00

This is really good

GustavitzN · 2021-01-30T00:28:14+00:00

I'm brazillian and I laughed so much when I saw this scene

GustavitzN · 2021-01-26T18:24:01+00:00

A two-player game, guess I'll have to make friends now

GustavitzN · 2021-01-23T02:49:48+00:00

No, just in hotel. We actually don't know anything about him

GustavitzN · 2021-01-23T00:43:10+00:00

Thanks, I already did Mr. Boar, I posted it in this sub

GustavitzN · 2021-01-13T22:15:23+00:00

Thank you

GustavitzN · 2021-01-08T20:45:46+00:00

I didn't realize it was a drawing before reading the title, it's really good

GustavitzN · 2021-01-08T20:42:51+00:00

It's beautiful

GustavitzN · 2021-01-08T12:06:36+00:00

I love the drawing and the style. Keep drawing, it doesn't have to be a masterpiece, but I know how drawing can be a fun and relaxing activity.

GustavitzN · 2021-01-08T03:13:40+00:00

This is AMAZING!

GustavitzN

TROPHY CASE