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In math class we recently learned that any number to the 0th power is one.
One, what the hell?

By placing a power over a number, you are abbreviating something like 2x2x2 to 2(3)...
We work our way down...
2x2 = 2(2)
2 = 2(1)
= 1? How do you get 1?


On the left side of the bottom equasion is nothing, and 0 is a representation for nothing. Whether it be a lack of a digit or any number at all, it means nothing. Since there is nothing on the left side, we can place a 0 there.

0=1

No, it doesn't work. I simply don't see why something(0) should equal 1.

Knowing there are a few higher level math geeks than myself here, could I get a hand? I must know how and why anthing(0) = 1!

ADDITION:
Since I have no cluse how to do miniature power numbers, any number in ()'s is a power....

Exponents are represented by the ^, something placed in parentheses means multiplication.

For example 2^3 is 8 while 2(3) is 6.

Think of it in terms of dimensions. A line is considered a one-dimensional figure, and for our purposes here let us say a single point is in zero dimensions. The point is a single value along the line of infinite values, and thus its value is 1 out of infinity.

Thus, x^0 = 1

I got this from wikipedia:http://en.wikipedia.org/wiki/Empty_product...o_the_0th_power

I know 2(3) = 6, I just couldn't find a way to represent powers, but now I know.


And anyway, the article says one is the result of multiplying no numbers, yet does not have anything to back this. 0x0=0....

ADDITION:
I'm going to bed, hoping for an answer in the morning.

Trying to keep this simple, if you add or subtract numbers represented by scientific notation, you'll sometimes find yourself using 10^0. It works as a transition between a number switching between a negative and postive exponent.

Example;

13.37*10^-2 = 1.337*10^-1 = .1337*10^0 = .01337*10^1, etc.
The represented number is .1337which is the same as .1337*10^0. Having a different exponent would require the base number be changed to comply with the rules of proper scientific notation.

That's the simplest kind of example I could come up with, I hope it helps you understand, :\

Let's see..

2^3 = 8
2^-3 = 1/8
And if you multiply them you get 1 .
Not sure if it's a super explanation, but it helps you think of it better. Negative numbers go into fractions, positive go into regular numbers, so 0 goes into the middle - 1.

Somethnig slightly related, is that I proved anything divided by 0 = -0, and not a true nonexistant number.

*Syphon attempts to remeber.

Hmmm...

*Syphon remeber he wrote it down on a recent math test.

Anyways, it has something to do with negative recipricals of slope.
(Not your thing, mine, yours' does have to do with negative denominators though.)

*Syphon grabs calculator and remebers arguments with grade 8 math teacher.

Basically I'm gonna do it like this, negative exponents.

2^1 = 2; 2^-1 = 0.5

Now that's just fine and good, but why?

2^1 = 1/2^-1
But othwise, it's just obviously 2.

2^-1 = 1/2^1
Which is, of course 0.5 .

Now to explain 0 I will just go 1/2^-0, which quite obvious is tricky, as -0 = 0, but not really. So basically 2^0 = 1 just because it does, which makes the rule of 1 divided by the -1(Exponent) work for 0. Now, as is painfully obvious, 1/1 = 1.

I wonder, is the following true?
X^-0 = -1

-1 would be i^2 (when algebra gets screwed...you'll use this alot in engineering...)
(i is a complex number)
http://en.wikipedia.org/wiki/Complex_number

x^-0 is the same as 1/(X^0) and would still be 1

^Soulshifter

No. Negative zero is the same as 0, and as such it's still x^0, which = 1. If it was -2x^0, then it would be -1, since with that you're doing -(x^0).

Which is exactly what i proved in my post

x^2 = x*x
x^1 = x
x^0 = x/x
x^-1 = 1/x
x^-2 = 1/(x*x)

It can be mathematically proven, but it's too much of a hassle for me to come up with a formula.

Man, look at Syphon go. And isn't -0 = 0*i ? i, if I'm not mistaken is an imaginary number and means that it is always negitive or something...

x^2 = xx
x^1 = x
x^0 = ?
x^-1 = 1/x
x^-2 = 1/xx

x^0 must be in the middle of x and 1/x. Let us input a number:

2^1 = 2
2^0 = __
2^-1 = 1/2

No since 2 = something and most of us know that something divided by nothing (x/0) is 'undefined' , we can't say we can't say that we even have 2, now can we, if we say that 2^0 equals nothing.

x/0 ≠ 0
x^0 ≠ 0
x*0 = 0

Now, let's show why x^0 = 1

x^1 = x
x^-1 = 1/x

x^1-1 = x^0 !!

x = 2
2^1-1 = 2^0 !!
2*1/2 = 1 or 2/1 / 1/2

So... 2^0 = 1

There... Phew... PLZ GOD LET THAT HAVE EXPLAINED IT!!! PLZ!!!

5^0 = 5 * 1/5, which equals 1. That's the only number to make it equal one, so that's my theory. I think I'll just stick with that .

Your assumption makes no logical sense and is wrong.



Why would 2(1/2) be used as proof?, it has no relation with the problem.

(2/1)/(1/2) = (2/1)(2/1) = 4

…
x[sup]3[/sup] = x*x*x
x[sup]2[/sup] = x*x
x[sup]1[/sup] = x
x[sup]0[/sup] = x/x
x[sup]-1[/sup] = x/x/x
x[sup]-2[/sup] = x/x/x/x
x[sup]-3[/sup] = x/x/x/x/x
…

That is why 0^x, where x<1 gives an error. X/0=error. (Undefined is what I learned in school, but my calc says "Domain" and computer says "devide by zero")

Basically,
x^2 = x*x*1
x^1 = x*1
x^0 = 1

Remember there's always that one in there.

Eh? I always thought of it as x/x, and that is why 0^X is an error. 0^0 ≠ 1
(I just guess from my small knowledge of math. After 3 years of Algebra I pass . At least I started Algebra a few years early so I am now just at the basic level)

I haven't been in a math class in a few days, I needed a fix of iris buring numbers and formulii.

Perhaps look at a logarithm?

Logx1 = 0

However:

{x|x≠0}

You cannot take a sublog of 0, so in that case:

0^0 ≠ 1

Everything else will equal 1:

x^0 = 1

1 can also be written as x to any exponent over itself, correct?

1 = [(x^3)/(x^3)]
x^0 = [(x^3)/(x^3)]
x^0 = [x^(3-3)]
x^0 = x^0

That is why anything, besides 0, to the exponent, 0, is equal to 1.

Ok, I have the best proof possible right here.

x[sup]2[/sup]/x[sup]2[/sup] = x[sup]2-2[/sup] = x[sup]0[/sup].
and since x[sup]2[/sup] = x[sup]2[/sup], and any number/sentence divided by itself is ONE, hence x[sup]0[/sup] = 1.

Problem solved.

Simplest way to think of it for me

Always remember, Feliz es tu madre!

Happiness is your mom?