To the power of zero; zero exponent

Cifrocco · #1 $Old$ 06-12-2008, 04:11 PM

I searched for a discussion of the rules governing exponents of zero but didn't find anything so I thought I'd start a thread on it.

We have learned that any number raised to the power of zero is equal to 1. Why is that so? Also, does this apply to zero, that is, zero raised to the power of zero?

Plato · #2 $Old$ 06-12-2008, 04:35 PM

To answer this question is beating a dead horse. But it is summer.
We know the rules of exponents: $\frac{{x^5 }}{{x^3 }} = x^{5 - 3} = x^2$ .
Therefore we would have to allow $1 = \frac{{x^5 }}{{x^5 }} = x^{5 - 5} = x^0$ .
But we never allow division by zero!
Therefore, it can be argued that $0^0$ is not defined.
But if you look at the first link, you will see that this is very old argument.
The great Euler argued that $0^0 = 1$ .

Math Forum: Ask Dr. Math FAQ: Zero to Zero Power
Math Forum: Ask Dr. Math FAQ: N to Zero Power

topsquark · #3 $Old$ 06-12-2008, 06:40 PM

I have heard of conventions stating that $0^0 = 1$ and $0^0 = 0$ . But these are just conventions used in specific cases to generalize a result. As Plato says, this is not a defined operation so it is undefined.

-Dan

Math's-only-a-game · #4 $Old$ 06-13-2008, 08:23 AM

Quote:

Originally Posted by Cifrocco $View Post$

We have learned that any number raised to the power of zero is equal to 1. Why is that so? Also, does this apply to zero, that is, zero raised to the power of zero?

(e^x) (e^0)= e^x+0 = e^x and hence e^0 = 1 for all e in the set R (Real numbers)

What is 0^0?? I asked my Maths Professor that question 15 years ago; His answer was: God knows

Plato · #5 $Old$ 06-13-2008, 04:47 PM

Quote:

Originally Posted by Math's-only-a-game $View Post$

(e^x) (e^0)= e^x+0 = e^x and hence e^0 = 1 for all e in the set R (Real numbers)

For all? Did you then divide by zero?

Math's-only-a-game · #6 $Old$ 06-14-2008, 01:04 AM

Quote:

Originally Posted by Plato $View Post$

For all? Did you then divide by zero?

Are you trying to say: If for all e in R then e = 0 ==> e^x = 0^0 = ??

Well spotted; I should have said "for all {R - 0}" i.e for all Real numbers except 0.

My Apologies

Btw I have sent you a private message; have you received it?? I was asking how do you type/copy/paste the maths text. I have try it with Mathcad, Math type 6 and Word with no success.

I would highly appreciate any help from anyone.

Plato · #7 $Old$ 06-14-2008, 06:07 AM

Quote:

Originally Posted by Math's-only-a-game $View Post$

[color=navy]Btw I have sent you a private message; have you received it?? I was asking how do you type/copy/paste the maths text. I have try it with Mathcad, Math type 6 and Word with no success.

Using MathType you can produce LaTeX code. Choose LaTeX tranlators found under Preferences. By coping an expression you get this code \[\frac{{\partial x}}{{\partial y}}\] which you then edit to [math]\frac{{\partial x}}{{\partial y}}[/math] to produce $\frac{{\partial x}}{{\partial y}}$ .

Math's-only-a-game · #8 $Old$ 06-14-2008, 06:40 AM

Quote:

Originally Posted by Plato $View Post$

Using MathType you can produce LaTeX code. Choose LaTeX tranlators found under Preferences. By coping an expression you get this code \[\frac{{\partial x}}{{\partial y}}\] which you then edit to [math]\frac{{\partial x}}{{\partial y}}[/math] to produce $\frac{{\partial x}}{{\partial y}}$ .

Thanks for the info. However I can't get the preferences options activated possibly because I have the free version. In other words to use the preferences options I would have to buy the software.

Thanks anyway. Much obliged

Plato · #9 $Old$ 06-14-2008, 07:49 AM

Quote:

Originally Posted by Math's-only-a-game $View Post$

I can't get the preferences options activated possibly because I have the free version. In other words to use the preferences options I would have to buy the software.

Even with the free version.,TeXAid, it works. Go to perferences, pulldown that tab the first option is Translators. Ckick translators an new window appears. Click translate to other languages(text). In the window below that select TeX--LaTex2.09 and later. Uncheck any boxes below that.

Math's-only-a-game · #10 $Old$ 06-14-2008, 09:07 AM

Quote:

Originally Posted by Plato $View Post$

Even with the free version.,TeXAid, it works. Go to perferences, pulldown that tab the first option is Translators. Ckick translators an new window appears. Click translate to other languages(text). In the window below that select TeX--LaTex2.09 and later. Uncheck any boxes below that.

That's exactly what I've tried but for some reason none of the options under preferences can be activated. Maybe the software is corrupted. I should try to re-download the software but I don't know if they will allow me to do so, for I used my free trial.

Thanks for your concern

Zack