Tuesday, December 25, 2018

exponentiation - What is 0 raised to 0 ???!!!!




I have read many articles on this confusion but i am still confused...



My simple question is -




What is $0^0$?



What is the present agreement to this?



I feel that it should be 1 as anything to the power zero is one....



I am currently a school student so i would like a more of a school based answer..



So incase it comes in my exam i should know what to write:)



Answer



$0^0$ is most often undefined. The reason is that it is not possible to define it in a good enough way. Notice the following examples:



$0^x$



Whenever $x \neq 0$ then this expression should equal to 0. However



$x^0$



should be $1$ whenever $x\neq 0$. Thus, if we define $0^0$ to either $0$ or $1$ then we get problems with these functions not being continous (without jumps if you plot them) where they are defined, which is why we keep $0^0$ undefined in most cases.



No comments:

Post a Comment

analysis - Injection, making bijection

I have injection $f \colon A \rightarrow B$ and I want to get bijection. Can I just resting codomain to $f(A)$? I know that every function i...