0

I am seeing some claims on the interwebs that $0^0$ is undefined, but also some claims that it is 1, which makes sense to me in terms of naive set theory:

$$0^0=\emptyset^\emptyset,$$ which is the set of functions from the empty set to itself, and since there is only one such function (viz, the empty function), then $0^0$ must be 1, correct?

Asaf Karagila
  • 393,674
Hank Igoe
  • 1,408
  • 1
    Then it is 1 in set theory and undefined in calculus; there is nothing unusual about it. – Ivan Neretin Dec 17 '22 at 10:04
  • 1
    There is no widely accepted convention what $0^0 $ should be. In many cases, it is useful to consider it to be $1$ since it is consistent with many important results – Peter Dec 18 '22 at 07:31

0 Answers0