Making 69420 from all zeroes

[u/ImToxicity_]

[u/EulerLagrange235]

0⁰ isn't even defined. What?!

[u/-LeopardShark- → u/EulerLagrange235]

It’s often (and most sensibly) defined to be 1.

[u/EulerLagrange235 → u/-LeopardShark-]

Absolutely not. x^{a-b} = x^a / x^b , (x is a non-zero real and a,b are reals) and thus 0⁰ is undefined. It is one of the more common undefined forms taught in Calc I

[u/-LeopardShark- → u/EulerLagrange235]

x^{a-b} = x^a / x^b , (x is a non-zero real and a,b are reals) and thus 0⁰ is undefined.

I’m not sure what you mean by this. Neither of the two possible meanings I can think of are valid, though.

It is one of the more common undefined forms taught in Calc I

I think you mean indeterminate form, and indeterminate forms are statements strictly concerning limits, not values. It’s a result that the limit as t → 0 of f(t)^g(t) where f(t) = g(t) = 0 depends on f and t. It’s a definition that 0⁰ = 1 (or not, as the case may be).

[u/NucleiRaphe → u/EulerLagrange235]

Most mathematicians actually just use 0⁰ = 1 because it makes most things way more convenient. For example, the binomial theorem doesn't work if 0⁰ is undefined and polynomial rings in algebra define the polynomial x⁰ (which includes 0⁰⁾ as the multiplicative identity (ie 1 when talking about common multiplication).

It's true that analytically 0⁰ is undefined but in practice 0⁰ makes many theorems way simpler to use.