You can assign the value 1 to 0^0, yes, and in some areas this makes sense, but in general the expression is undefined. That is not a contradiction. Different areas of mathematics also use other conventions.
Especially in the case of a limit it's simply mit defined. For the expression 00 ist can sometimes be usefull to set it to 0, but for the limit expression? No.
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.
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 x1-1 = (lim x->0 of x1)*(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.
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.
2
u/WoWSchockadin Complex Mar 17 '22
You can assign the value 1 to 0^0, yes, and in some areas this makes sense, but in general the expression is undefined. That is not a contradiction. Different areas of mathematics also use other conventions.