Hello, I'm a friggin moron! (OT)

Coast to Coast SC

Registered User
Well, it happened, a 7th grader just stumped me with a math problem...a little help please? Exponents are an expression of multiplication strings so 4^3=4x4x4=64. Now there is a rule that any # to the power of zero is one (there is a logical proof out there that I learned in the first year of my EE program, but my mind fails me at this point) so A^0=1 and logic would have it that 0 to any power is 0 -> 0^B=0 Here comes the 13 year old ready to stump the teach...0^0=? I probaly could have BS'd my way through something but I'm not really into that so I was hoping one of you guys who have done this shtuff more recently could refresh my memory. Thanks!

Anthony

In short, what is 0^0=
 
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Hey Coast to Coast,

Here is my solution but dont ask me to explain it much more than this:

When you plot the function f(x)=0^x for x>1 your solution for any positive number is 0.

For x<0 (negative numbers) your solution will always be infinity because you will have division by zero, ie f(x)=a^-x = 1/(a^x) therefore if a=0, the bottom part of that fraction (a^x) would be equal to 0 (because it is of the form stated in the top part of this explanation) and that would ultimately be division by 0. Thus for all negative numbers the function (f(x)=0^x ) is infinity.

If it were true that 0^0=1 then that would mean that f(x)=0^x for x=0 would be 1 (1/(1)=1) and for every other positive value it would be 0. So it neither follows the limits of being a negative number or a positive number and mathematics calls it undefined instead of infinity.


So basically it is undefined because 0 is neither positive or negative (0 is an assymptote on the x axis when you plot the function absolute value of x)
 
That works!

Thanks Al. That was right on the money of what I was after. Don't worry, I'll give full credit to you when I pass it on to the kids on Monday!

Anthony
 
Well, its sorta right, but it doesnt explain it well. So use your jedi powers to make it sound more eighth grader friendly.

Al
 
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