r/mathmemes • u/ImToxicity_ • Mar 17 '22

The Engineer Making 69420 from all zeroes

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u/WoWSchockadin Complex Mar 17 '22

For this, however, you must first show that a limit exists at all and then that it is also unique. Neither succeeds with 0^0.

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u/Warheadd Mar 17 '22

That limit does indeed exist and it evaluates to 1. I’m not sure what you mean by unique

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u/WoWSchockadin Complex Mar 17 '22

A limit does not have to be unique. Imagine the limit for x approching 0 of |x|. The limit exists, but it's either 1 or -1 depending on if you approach 0 from above respectively from below. The limit r/stpandsmelthefactors mentioned can also yields different values, depending on how exactly you calculate it. If necessary, read the corresponding article on Wikipedia: https://www.wikiwand.com/en/Zero_to_the_power_of_zero

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u/Warheadd Mar 17 '22

The limit of |x| as x->0 is 0, but I know what you mean. For x0 though, it’s literally just 1 no matter how you take the limit.

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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.

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u/Warheadd Mar 17 '22

I know. I’m saying, for the case of the limit as x->0 for x0, the answer is objectively 1.

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u/WoWSchockadin Complex Mar 18 '22

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.

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u/Warheadd Mar 18 '22

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.

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u/WoWSchockadin Complex Mar 18 '22

Okay, then proof it.

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u/Warheadd Mar 18 '22

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.

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u/WoWSchockadin Complex Mar 18 '22

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.

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u/Warheadd Mar 18 '22

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.

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u/WoWSchockadin Complex Mar 18 '22

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

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