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## #1 2007-05-24 19:05:13

Daniel123
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### Power of 0

I am having trouble understanding how x°=1, for any value of x.

I can understand it algebraically:

x^m ÷ x^m = 1

x^m ÷ x^m = x^m-m = x°

∴ x° = 1

But I cannot understand how any number multiplied by itself 0 times would give 1? It doesn't make much sense logically to me. Can anyone explain how this works (bearing in mind i am 15 - so not too complicated please)?

Thank you.

Last edited by Daniel123 (2007-05-24 19:05:44)

## #2 2007-05-24 19:14:29

luca-deltodesco
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### Re: Power of 0

well, easiest way to think about is to look at it like a series:

as you go down the series, you divide by n, n/n = 1
as you go up the series, you multiply by n, 1/n*n = 1

example there, as you go down, you divide by 2, 8->4->2->1->0.5->0.25
same going up, the only number that makes sense is 1.

the only time it doesnt really apply is in 0^0, but to keep it consistent, we say that 0^0 = 1 aswell, although often, youll just see it as undefined aswell.

Last edited by luca-deltodesco (2007-05-24 19:16:41)

The Beginning Of All Things To End.
The End Of All Things To Come.

## #3 2007-05-24 19:21:52

mathsyperson
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### Re: Power of 0

This 0^0 thing really confuses me. It needs to be 1 to be consistent with Luca's sequence, but then it breaks this one:

0^3 = 0
0^2 = 0
0^1 = 0
0^0 = 1?

And to add even more confusion in there, as well as arguing whether it's 0 or 1, some people say that it's neither. But then those people argue about whether it's undefined or indeterminate.

Why did the vector cross the road?
It wanted to be normal.

## #4 2007-05-24 19:29:10

Daniel123
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### Re: Power of 0

Ok so i can now see why x°=1

but you have totally confused me with the 0^0 thing!

Thats given me something to think about!

Thanks.

## #5 2007-05-24 19:56:26

Daniel123
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### Re: Power of 0

Im just wondering, in other bases, e.g. base-6, would 0 have the same value? I find it imposible to understand other bases.... and just out of curiosity, why did we choose base-10? Would mathematical rules still be the same if other bases were used?

## #6 2007-05-24 23:36:14

MathsIsFun

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### Re: Power of 0

To understand other bases I made a simple little "base counting" flash thingy here: Binary, Decimal and Hexadecimal Numbers

(Look for "Why not try it yourself?", and then make the thing count for you in base-2 then base-3 etc up to base-10)

"The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  - Leon M. Lederman

## #7 2007-05-24 23:40:36

Ricky
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### Re: Power of 0

Typically, 0^0 is left undefined.

As for bases, think of numbers simply as symbols.  So we start out defining "1" as the symbol for the first number (integer).  Then we define the symbol "2" to stand for 1 + 1.  And "3" simply means "2 + 1", or rather, "1 + 1 + 1".   And so on.

So it makes no difference whether you use 0101 to represent 5 in binary, or 387 to represent 322 in base 9.  They are just symbols and nothing more.

We most likely use base 10 because of the 10 digits (fingers) we have.  But other cultures have used things such as base 60 in the past.

Why do computer scientists always get Halloween and Christmas mixed up?

'Cause 31 (Oct) = 25 (Dec)

"In the real world, this would be a problem.  But in mathematics, we can just define a place where this problem doesn't exist.  So we'll go ahead and do that now..."

## #8 2007-05-24 23:48:51

Daniel123
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### Re: Power of 0

Thanks both of you it has really helped my understanding

## #9 2007-05-25 00:11:15

Sekky
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### Re: Power of 0

#### Ricky wrote:

Typically, 0^0 is left undefined.

The exponential series equates it to one, which I believe is the limit, rather than zero.
Neither here nor there really

## #10 2007-09-09 22:33:25

landof+
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### Re: Power of 0

Ignoring official laws, I'd say x^0 where x is a number, is typically 0, because take a. a multiplied 0 times is:

.... Or nothing. Proven.

I shall be on leave until I say so...