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- CommentAuthorhero
- CommentTimeApr 1st 2007 edited
I was looking through my notes from class, and i realized that i was still unsure about something. I am not sure about how x(to the zero-ith power? ) always equals 1. Especially if x equals 0.

I know that brilliant people are on this site, and I was wondering if you would help me.
- CommentAuthorcmseagle
- CommentTimeApr 1st 2007 edited
It's because of the pattern.

10^5=100000
10^4=10000
10^3=1000
10^2=100
10^1=10
10^0=1
- CommentAuthorHaoest
- CommentTimeApr 1st 2007
http://oakroadsystems.com/math/expolaws.htm#Zero
- CommentAuthorandresoforo
- CommentTimeApr 1st 2007
If x^0=0, then that would mean that anything^anything=0
- CommentAuthorcmseagle
- CommentTimeApr 1st 2007
Not necessarily, it would mean that x^anything=0
- CommentAuthorandresoforo
- CommentTimeApr 1st 2007
Yes. That is what I mean. Thank you my dear colleague.
- CommentAuthorjsimpleton
- CommentTimeApr 1st 2007
um... 0^0... is undefined...
- CommentAuthorjsimpleton
- CommentTimeApr 1st 2007
math is hard, we should ban math
- CommentAuthorHaoest
- CommentTimeApr 2nd 2007 edited
LOL. I vote jsimpleton for admin of this thread. He's math TA
- CommentAuthorhero
- CommentTimeApr 2nd 2007
Hm. So is 0^0 undefined? Or is it 1?
- CommentAuthorHaoest
- CommentTimeApr 2nd 2007
It's undefined because jsimpleton said so.

don't forget where you are, buddy
- CommentAuthorcmseagle
- CommentTimeApr 2nd 2007
Posted By: Haoest
It's undefined because jsimpleton said so.

don't forget where you are, buddy

I mean, on this site, when someone says something, it's essentially law. Like you said, this website has one of the highest concentration of superior cognitive people of anywhere I've found. I would believe what people say.
- CommentAuthorandresoforo
- CommentTimeApr 2nd 2007
Posted By: hero
Hm. So is 0^0 undefined? Or is it 1?

It equals One.
- CommentAuthorUdoboy
- CommentTimeApr 2nd 2007
0⁰ is undefined.
- CommentAuthorStrugs
- CommentTimeApr 2nd 2007
I find this the easiest way to think of it. you have to keep in mind that a can be expressed as 1a.

"Notice that a^b can be thought of as "start with the number 1, then multiply by a, b times." For instance, a^2 = 1 x a x a and a^1 = 1 x a . Therefore, a^0 should be just 1, not multiplied by anything else at all."
This is from
http://www.math.utoronto.ca/mathnet/questionCorner/powerof0.html

Sorry if I haven't cited this properly, I'm new here.
- CommentAuthorHaoest
- CommentTimeApr 2nd 2007
Obviously...
- CommentAuthorTephy
- CommentTimeApr 3rd 2007
0^0 = 1. Well, it is approaching one and if it could exist it would be one. This is a limit. For example, what is 0.000000000000000000000000000000001^0? 0.99999999999999999999999 or whatever, very close to one. Try graphing x^0 on your calculator and you'll see that at 0, y = 1. It doesn't actually exist, but if it did, it would be equal to one.

Thank you calculus!
- CommentAuthorjsimpleton
- CommentTimeApr 3rd 2007
Posted By: Tephy
0^0 = 1. Well, it is approaching one and if it could exist it would be one. This is a limit. For example, what is 0.000000000000000000000000000000001^0? 0.99999999999999999999999 or whatever, very close to one. Try graphing x^0 on your calculator and you'll see that at 0, y = 1. It doesn't actually exist, but if it did, it would be equal to one.

Thank you calculus!

.... that is so very wrong....
- CommentAuthorYika
- CommentTimeApr 4th 2007
But oh so fun!
- CommentAuthoro999
- CommentTimeApr 7th 2007
The way I like to think of why x^0 = 1 (x<>0) is using the exponent rules:

(x^a)/(x^b) = x^(a-b) [as long as x <> 0], therefore (x^a)/(x^a) = x^(a-a) = x^0 = 1
- CommentAuthorFact totum
- CommentTimeApr 7th 2007
There was a time when I would have thought that was cool. Now ... well, it gives me a headache.

(Actually, it doesn't. I'd explicitly point out that a number divided by itself, such as (x^a)/(x^a), is equal to 1. Very good explanation.)
- CommentAuthorjsimpleton
- CommentTimeApr 7th 2007
to summerize: x^0=1 if x!=0
if x=0 then x^0 is undefined

we should really move. how about them prime numbers?
- CommentAuthorTephy
- CommentTimeApr 7th 2007
Haha, whoops, I have no idea what I was talking about jsimpleton. It was early in the morning and I realize my error. 0^0 is undefined, but if it could exist, it's equal to 1.
- CommentAuthorslithytove2
- CommentTimeApr 13th 2007
x^0 is defined as 1 for all real numbers x not equal to 0. => 0^0 is undefined
when x^0 comes up, its usually taking a limit, so the limit depends on the rest of the statement.

same thing with division
0/x is 0
x/0 is undefined
0/0 is ??
if you graph y=sin(x)/x, you will see that at 0, the line crosses x=0,y=1 but its actually undefined.
limit as x->0 of sin(x)/x is 1, but sin(0)/0 is undefined
- CommentAuthorestebanissexy
- CommentTimeApr 14th 2007 edited
I sure do like them prime numbers
lets list them, starting at 111
- CommentAuthorestebanissexy
- CommentTimeApr 14th 2007
111
- CommentAuthorUdoboy
- CommentTimeApr 14th 2007
Posted By: slithytove2
x^0 is defined as 1 for all real numbers x not equal to 0. => 0^0 is undefined

All natural numbers. A real number, such as π, does not have a factorial.

Posted By: estebanissexy
I sure do like them prime numbers
lets list them, starting at 111

111 is not prime; it is divisible by 3.
- CommentAuthorCody56
- CommentTimeApr 15th 2007
What is Plato's triangle? I've searched the internet and found nothing...
- CommentAuthorAthene
- CommentTimeApr 15th 2007
It was the only instrument he knew how to play. (Brilliant philosopher, crappy musician...)
- CommentAuthorKasNZ
- CommentTimeApr 16th 2007
Any real number (positive or negative, rational or irrational) except zero, raised to the power of zero, equals one. Any expression yeilding a real number solution not equal to zero, equals one. Pi raised to the power of zero equals one.
(1.0E-99)^0 = 1
(-1.0E-99)^0 = 1
The reason? See the comment from o999 dated 7 Apr.
See also the comment from cmseagle dated 1 Apr.
So why does 0^0 not equal 1? A simplified explaination uses o999's observation, and highlighted by Fact totum: Anything divided by itself equals 1 - EXCEPT ZERO, because division by zero is undefined.
Note that if you divide any constant numerator (the top number in a fraction) by an increasingly smaller denominator (the bottom number in a fraction), the quotient (the result of a division - which is what a fraction is) gets increasingly larger. Immagine that the denominator becomes as close to zero as possible without equaling zero, the quotient becomes almost infinitly large. Now immagine the denominator actually reaching zero - the quotient would be infinity, and infinity as a mathematical concept is undefined! Where were you in your 10th grade math class??
PS - For those of you that are into such things: Do not get FRACTIONs (divisions) confused with VULGER FRACTIONs(ratios). It is a different thing! (Although most people think all fractions are vulger in concept!!)
- CommentAuthorestebanissexy
- CommentTimeApr 16th 2007
Posted By: Udoboy
Posted By: slithytove2
x^0 is defined as 1 for all real numbers x not equal to 0. => 0^0 is undefined

All natural numbers. A real number, such as π, does not have a factorial.

Posted By: estebanissexy
I sure do like them prime numbers
lets list them, starting at 111

111 is not prime; it is divisible by 3.

damn
- CommentAuthorKasNZ
- CommentTimeApr 17th 2007
Incidental to my missive of 16 Apr:
I know that there are misspellings. If I could spell, perhaps I would teach English rather than Mathematics. Of course, this begs the question, “Where was I during 10th grade English class?” Apparently, studying Math! Oh well – as long as we keep it lighthearted . . .
- CommentAuthortezza98
- CommentTimeApr 23rd 2007
A simple mathematic proof

3^5 = 3^6 ÷ 3 = 243
3^4 = 3^5 ÷ 3 = 81
3^3 = 3^4 ÷ 3 = 27
3^2 = 3^3 ÷ 3 = 9
3^1 = 3^2 ÷ 3 = 3

Then logically

3^0 = 3^1 ÷ 3 = 3 ÷ 3 = 1.
and the case for 0
0^0 = 0^1 ÷ 0 = 0 ÷ 0 = undefined

negative powers
3^-1 = 3^0 ÷ 3 =1/3 etc
- CommentAuthorHaoest
- CommentTimeApr 24th 2007
I heard there are many ways to prove that
0.999... (9 repeats forever) equals 1.

One of the presidents of the United States (I have hard time remembering, maybe it was Richard Nixon??) proved this is true in his own way.
- CommentAuthorCody56
- CommentTimeApr 24th 2007
Right here, ol' chap (I'm saying that a lot lately...)
- CommentAuthorUdoboy
- CommentTimeApr 24th 2007
A ninja hidden in the hyperlink? Hmm
- CommentAuthorCody56
- CommentTimeApr 24th 2007
Those sneaky ninjas!!!
- CommentAuthorjsimpleton
- CommentTimeApr 24th 2007
someone do Euler's proof of infinite primes, its a good one
- CommentAuthorhero
- CommentTimeApr 25th 2007
That .9 repeating is equal to one is quite an interesting article.
- CommentAuthornyarfdude
- CommentTimeApr 25th 2007
Math is like love; a simple idea, but it can get complicated.
- CommentAuthorHaoest
- CommentTimeApr 26th 2007
Can you elaborate that?
- CommentAuthornyarfdude
- CommentTimeApr 26th 2007
Nope.
- CommentAuthorhero
- CommentTimeApr 26th 2007
Oh.
- CommentAuthorYika
- CommentTimeApr 26th 2007
el oh el
- CommentAuthorCody56
- CommentTimeApr 26th 2007
I THINK I KNOW LEGAT'S SIDE ACCOUNT!!!! IT'S HERO!!!!! I mean come on, his name is kyle... and he only has 8 posts!!!
- CommentAuthorCody56
- CommentTimeApr 26th 2007
And besides... I never see them on at the same time!!
- CommentAuthorTrance
- CommentTimeApr 26th 2007
You could have had a lot more fun there.
- CommentAuthorYika
- CommentTimeApr 26th 2007
OH LORDS GIVE U THE NO-BELL PRIZE!
- CommentAuthorCody56
- CommentTimeApr 26th 2007
Posted By: Trance
You could have had a lot more fun there.

?
- CommentAuthorTrance
- CommentTimeApr 26th 2007
You could have screwed with him, man!

But come to think of it, would Kyle put his real name in his side account?

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Citation Station: Math Help