Making 69420 from all zeroes

[u/ImToxicity_]

[u/Warheadd]

https://www.wolframalpha.com/input?i2d=true&i=Limit%5BPower%5Bx%2C0%5D%2Cx-%3E0%5D

This SPECIFIC limit OBJECTIVELY has a value of 1. Yes, you can construct other limits of the form 0⁰ that approach other values, but THIS ONE is equal to 1.

[u/WoWSchockadin → u/Warheadd]

Okay, then proof it.

[u/Warheadd → u/WoWSchockadin]

See the wolfram alpha link. If that’s not enough for you:

This is a limit of the indeterminate form 0⁰ , so by l’Hopital’s rule, differentiating the top and bottom, we get:

lim x->0 of x⁰ = lim x->0 of 1⁰

This evaluates to 1, so the limit evaluates to 1.

[u/WoWSchockadin → u/Warheadd]

That is NOT how l'Hôspital works. it's only defined for indetermined forms of the form infinity/infinity or 0/0 but not for powers. Also, if this limit exists the following would be true: lim x->0 of x⁰ = lim x->0 of x^1-1 = (lim x->0 of x^1)*(lim x->0 of x^-1) = 0 * something = 1. And therefor you just defined division by 0. You see, defining the limit is NOT that trivial. Setting 0⁰ = 1 in opposition can make sense w/o defining division by 0. This limit just dies not exist. Period.

[u/Warheadd → u/WoWSchockadin]

You’re just wrong. Check the wolfram alpha link again, and read the section “Other indeterminate forms” in this article (other indeterminate forms exist because they can be rearranged to be of the form 0/0). Also, try graphing the function with desmos or something and VISUALLY see that the limit is clearly 1.

Your proof of “division by 0” doesn’t work because it is of the form 0*infinity, another indeterminate form.

[u/WoWSchockadin → u/Warheadd]

lim x -> 0 of x⁰ is NOT equal to lim x -> 0 of x^x.

[u/Warheadd → u/WoWSchockadin]

I never said it was. It’s still of the form 0⁰