0 to the power of 0 - Chess Forums

Deepak_oct

Mar 3, 2023

0

#1

So, why is 0 to the power of 0 = 1?

https://www.youtube.com/watch?v=r0_mi8ngNnM

Why does the value grow after decreasing?

Lincoy3304

Mar 3, 2023

0

#2

Well that’s controversial. Anything to the power of 0, by following a pattern, is that number divided by itself.
2^4=16
2^3=8
2^2=4
2^1=2
2^0=1
If you go down the line, you see that you divide that number by the base.
That means x^1/x^1=1=x/x
0^0 is defined as indeterminate by most mathematical researchers (because it’s 0/0), but there are times in which it is useful to see it as one, and times in which it is useful to see it as zero.

Deepak_oct

Mar 3, 2023

0

#3

Lincoy3304 wrote:

Well that’s controversial. Anything to the power of 0, by following a pattern, is that number divided by itself.
2^4=16
2^3=8
2^2=4
2^1=2
2^0=1
If you go down the line, you see that you divide that number by the base.
That means x^1/x^1=1=x/x
0^0 is defined as indeterminate by most mathematical researchers (because it’s 0/0), but there are times in which it is useful to see it as one, and times in which it is useful to see it as zero.

Deepak_oct

Mar 3, 2023

0

#4

I don't think it is undefined.

Lincoy3304

Mar 3, 2023

0

#5

Google’s calculator only does computation.
If we follow the pattern of 0^x where x is any real positive number, then all possible values of x will yield 0, regardless. Since two patterns of equal cardinality disagree with each other, there are two possible answers, leaving it indeterminate. Google’s calculator gives 1, but there are other senses where it equals 0. Google probably programmed their calculator where any x^0=1 and forgot to put display error when x=0. Google isn’t truth. Type 0^0 into WolframAlpha then tell me what you get. It’s not 1.

Intellectual_26

Mar 3, 2023

0

#6

If x^0 equals y. Then y will equal any number, for x at 0.

Lincoy3304

Mar 3, 2023

0

#7

By the technical definition yes intellectual. There are actually four patterns for approaching 0^0.
1: Divide by 0 until you get to zero to the power of 0, which is indeterminate.
2: Put everything to the power of 0, see the pattern, apply it to 0^0.
3: Put 0 to the power of all positive deals. See the pattern, apply it to 0.
4: Set everything to x^x. Take the limit at x->0. It approaches 1
Since 4 patterns exist for it, we must define it as indeterminate.