Zero^(zero)

Why is 0^(0) undefined?

Explain.

 

Zero to zeroth power is often said to be "an indeterminate form", because it could have several different values.

Since x^0 is 1 for all numbers x other than 0, it would be logical to define that 0^0 = 1.

But we could also think of 0^0 having the value 0, because zero to any power (other than the zero power) is zero.

Also, the logarithm of 0^0 would be 0*infinity, which is in itself an indeterminate form. So laws of logarithms wouldn't work with it.

So because of these problems, zero to zeroth power is usually said to be indeterminate. However, if 0^0 power needs to be defined to have some value, 1 is the most logical definition for its value.

In algebra and combinatorics, the generally agreed upon value is 0^0 = 1, whereas in mathematical analysis, the expression is sometimes left undefined.

 

This is good information for any math person.

 

What is combinatorics?

 

the branch of mathematics dealing with combinations of objects belonging to a finite set in accordance with certain constraints, such as those of graph theory

 

I never took this course.