- #1
The Rev
- 81
- 0
I've been told that any number raised to the zeroeth power is equal to 1. What about zero raised to the zeroeth power? Is that 1 or 0?
[tex]0^0=1?[/tex]
The Rev
[tex]0^0=1?[/tex]
The Rev
...and indeterminate. In some cases when a generalization is desired, it is profitable to define it as 1, in others, as 0.The Rev said:I've been told that any number raised to the zeroeth power is equal to 1. What about zero raised to the zeroeth power? Is that 1 or 0?
[tex]0^0=1?[/tex]
The Rev
That's not mathematical at all. I've always had a simple way of looking at it:CRGreathouse said:I don't think that it's undefined; I think that it's 1. 0^0 is an empty product, and empty products are necessarily equal to 1. As Galileo points out above, we need 0^0=1 for series to have compact formulas.
Everyone agrees that [tex]x^0=1[/tex] for [tex]x\neq0[/tex], but there's no reason to think that it should be different at 0 -- [tex]0^x[/tex] is only 0 for x > 0, since it's not defined for negative x.
There's no problem accepting 0^0 as 1, and there are many good reasons to think it shouldn't be undefined or 0.
Icebreaker said:What about [tex]x^x[/tex] as [tex]x \rightarrow 0[/tex]? I have always found [tex]x^x[/tex] fascinating for some obscure reason.
It is a very nice function though, when I first was thinking about it I tried to think about it in 4D in complex space and was pleasantly surprised when I started graphing it on mathematica recently I had quite a good idea oh how it looked.Icebreaker said:What about [tex]x^x[/tex] as [tex]x \rightarrow 0[/tex]? I have always found [tex]x^x[/tex] fascinating for some obscure reason.
Zurtex said:That's not mathematical at all. I've always had a simple way of looking at it:
[tex]x^0 = \frac{x}{x}[/tex].
No, I meant your approch to the problem.CRGreathouse said:Empty products aren't mathematical?
Zurtex said:No, I meant your approch to the problem.
Hurkyl said:I'm pretty sure the limit dex quoted goes to 1, not -∞.
BenGoodchild said:The fallacy comes right at the end when dividing by 0. So, we cannot divide by zero, and 0^0 is 0/0 therefore it is Mathematically undefined.
dextercioby said:Yes,but [tex] x^{0}=\frac{x}{x} \Leftrightarrow x\neq 0 [/tex].So master coda was right.
BenGoodchild said:So, we cannot divide by zero, and 0^0 is 0/0 therefore it is Mathematically undefined.I say we cannot divide by zero,
and as x^0 is x/x
which becomes, when x = 0, 0/0 cannot be omputed if we cannot divide by 0 it either doesn't exist or as I put it it is mathematically undefined.
Regards,
Ben
BenGoodchild said:I understand that this is true, and is infact what i said.
I say we cannot divide by zero,
and as x^0 is x/x
which becomes, when x = 0, 0/0 cannot be omputed if we cannot divide by 0 it either doesn't exist or as I put it it is mathematically undefined.
Regards,
Ben
Leopold Infeld said:I thought x^0 was x^(m-n) where m=n, so x^0 = x^m/x^n. If x=0, then
0^0 must be 0/0 = undefined.
Correct me if I am wrong.
I thought x^0 was x^(m-n) where m=n,