What's the answer actually? Zero? One? Undefined?
How do you prove your answer?
2006-08-21 15:25:22 · 19 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
Prove the answer? Sure...
Anything raised to the zero power is one, right?
But zero raised to any power is zero, right?
So, which is it?
The correct answer is that zero raised to the zero power is an indeterminate form.
In math, if there is no possible correct answer to a problem (such as 6 ÷ 0), it's undefined. This case, though, there are possible proofs to show two different answers are legal. That's why it's indeterminate (not undefined).
Indeterminate forms lead to interesting ways to find limits and derivatives when you get to the calculus, but until you get there, you don't have to worry about it. Zero to the zero power is an indeterminate form, and you can leave it at that.
2006-08-21 15:52:46 · answer #1 · answered by Anonymous · 1⤊ 0⤋
This question seems to get asked every 3 or 4 days.
0^0 is undefined since, if you say it's 1, then that implies
(0^1) / (0^1) = 0^(1-1) = 0^0 =1 But
(0^1) / (0^1) = 0/0 = undefined.
The moral of the story is that you have to be kinda careful when you start using 0's around divisions and exponentiations
Doug
And to coolsober: Yes 0! = 1 by definition because a lot of indicial equations start off with a 0 index. It's just a convention that makes things a bit more compact and easier to write.
2006-08-21 15:48:45 · answer #2 · answered by doug_donaghue 7 · 2⤊ 1⤋
0/0 is undefined. But 1/0 is not undefined (as someone here suggests above---but he's got thumbs downs so i guess its ok)
0^0 would be 0^(1-1) = 0^1 * 0^-1
0^1 = 0 and 0^-1 = 1/0
therefore 0^0 = 0^(1-1) = 0 / 0 which is an undefined quantity in maths.
2006-08-22 22:47:54 · answer #3 · answered by blind_chameleon 5 · 0⤊ 0⤋
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2016-12-14 09:37:35 · answer #4 · answered by vazid 4 · 0⤊ 0⤋
I was wondering about the symbol ^. The closest that I came to it is in the American Heritage Dictionary page 1303. The last one looks like the one you are using and the dictionary called it a caret. I looked it up and it says it is a symbol used in proofreading.
What are you using it for? 0°x 0° = 0° or Zero power times zero power equals zero power. I know I am using a degree sign but yours is a proofreading sign and I guess it doubles for another also.
2006-08-26 13:13:26 · answer #5 · answered by Pepsi 4 · 0⤊ 0⤋
0^0 is an exception to the rule that something to the zero power is 1.
2006-08-21 17:16:14 · answer #6 · answered by ronw 4 · 1⤊ 1⤋
Let's see. I know that a number raised to the zero power is one, but zero itself...? Hmmm. The usual way of showing that some number to the zero power is one is by showing that subtracting the exponent is the same as dividing. And zero can neither be divided nor divide anything. So zero to the zero power is undefined.
2006-08-21 15:49:09 · answer #7 · answered by cdf-rom 7 · 0⤊ 2⤋
every number if powered 0 is 1 lets prove it
ok did u ever calculate postulates of ! fictorial like 3! = 3*2*1*0^0 = 6
hence proved
2006-08-21 15:38:13 · answer #8 · answered by Anonymous · 0⤊ 1⤋
0^0 = 0^(2 - 2) = 0^2/0^2 = 0/0.
Therefore, 0/0 is undefined.
2006-08-21 15:32:01 · answer #9 · answered by alnitaka 4 · 0⤊ 0⤋
0^0=1
See: http://en.wikipedia.org/wiki/Empty_product and the google link given above. Now naturally google and wikipedia are considered the twin repositories of all knowledge and wisdom, so if they both agree on the answer, it must be true.
2006-08-21 15:55:05 · answer #10 · answered by Pascal 7 · 0⤊ 1⤋