0 to 0th power?

[Tim_Lou]

take out your calculator,
put 0^0, it says error,

but is it really an error?

what does 0^0=?
i heard it in a forum saying that in the graph n^0, the lim of 0 is 1,
so it actually = 1,

also, it says that the graph of 0^n is rather unimportant...
what do you think?

[Tim_Lou]

consider this,

a^b/a^b = a^0 =1, so

0^x/0^x = 0/0..

after a little research on the internet, i found most of the time it is said that 0^0 is undefined.

however:
http://www.google.com/search?q=0%5E0&btnG=Google+Search


http://us.metamath.org/mpegif/exp0.html


these 2 sites say that it=1
the 2nd one is totally... un-understandable, maybe somebody could explain it...?

[TeleMad]

Tim_Lou: consider this,

a^b/a^b = a^0 =1, so

0^x/0^x = 0/0..

Look up the definition of that exponential rule and see if it excludes 0 (that is, say a is not equal to 0). For example, one of the math books I have states:

Quotient Rule for Exponents
a^m / a^n = a^(m - n), a != 0

another says

The Quotient Rule
For any nonzero number a and any positive interges m and n,
a^m / a^n = a^(m - n)

So you can't use the quotient rule of exponents to try to show that 0^0 = 1.


The reason for the restriction a != 0 is obvious (as you showed). Use a = 0 and say m = 5 and n = 3. That appears to give

0^5 / 0^3 = 0^(5 - 3) = 0^2 = 0.

But actually, it doesn't. Note that in the denominator 0^3 = 0, and you can't divide by 0. So when you use a = 0, you actually get undefined.

[Tim_Lou]

so, it is undefined... i think so too...

wait a minute:
a != 0 ????
??? how is it possible???
0! =1
1! =1
....

in a combination or permutation, there is always at least 1 possibility....