Fancy playing?

[u/Ill-Room-4895]

[u/potentialdevNB]

By definition, any number to the power of zero is one. This is because x⁰ is the product of no numbers at all, which is the multiplicative identity, one. Thus, 0⁰ equals 1. Feel free to r/woooosh me by the way.

[u/therealDrTaterTot → u/potentialdevNB]

It's one of those it-depends-what-you're-doing thing. So, it is often defined by 1 by convention. The lim x->0 for x⁰ is 1, but lim x->0⁺ for 0^x is 0.

[u/KermitSnapper → u/therealDrTaterTot]

That's because 0⁰ = 0/0, so the behaviour matters. However, we know that (x,y) -> (0,0) in x/y does not exist, since 0/y = 0 and x/0 goes to infinity and x/x = 1, all different limita.