zero by power of zero: Why does zero by zero equal to 1 and not to 0?

shahar said:
Why does zero by zero equal to 1 and not to 0?
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I take it you mean, why is zero raised to the zeroth power, that is, [imath]0^0[/imath], taken to be 1 and not 0.

Tell us why you think it should be zero, and then why you think it is actually 1. That is, who told you that?

If you've done sufficient searching, you should have found that it is taken to be 1 only under certain circumstances.
 
Dr.Peterson said:
I take it you mean, why is zero raised to the zeroth power, that is, [imath]0^0[/imath], taken to be 1 and not 0.

Tell us why you think it should be zero, and then why you think it is actually 1. That is, who told you that?

If you've done sufficient searching, you should have found that it is taken to be 1 only under certain circumstances.
Click to expand...
Question: Is every empty product is equal to 1?
(I don't understand by clearly by reading Wikipedia)
 
shahar said:
As wikipedia defines it with no factors to multiply.
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Ah! So it is essentially a problem where you are multiplying nothing by nothing.

Logically it could probably be equally useful to define it as 0. I suspect that there is some advantage in defining it to be 1, but I don't know what that advantage might be. (Usually, if we have an empty anything we try to define it to be 1 or a unit or some such.)

-Dan
 
shahar said:
Why does zero by zero equal to 1 and not to 0?
Click to expand...

For the sake of others who may come across this thread, the original question appears to be meant as follows:

Why is zero raised to the zero power equal to 1 and not to 0? That is, why is [imath]0^0 = 1[/imath]; why is [imath]0^0 \neq 0[/imath]?
Click to expand...
 
stapel said:
For the sake of others who may come across this thread, the original question appears to be meant as follows:
Click to expand...
Actually, according to post #4, he meant the empty product, which I think is what you get when you multiply nothing (not zero) by... well, there is no other factor.

Kind of like the limericks:
There once was a man from Perdue,
Who's limericks would end at line two!

and
There once was a man from Verdun...

ending it ruins the poem.

I've never heard of it, and I can't think of any use for it, but hey, after looking at Category Theory a couple of times, nothing surprises me anymore!

-Dan
 
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