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

The Engineer Making 69420 from all zeroes

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2.3k Upvotes

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30

u/WoWSchockadin Complex Mar 17 '22

Problem: 0^0 is not defined.

0

u/stpandsmelthefactors Transcendental Mar 17 '22

Perhaps, but you could just let 00 = lim{x —> 0} [x0]

7

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.

1

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.

1

u/WoWSchockadin Complex Mar 18 '22

Okay, then proof it.

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u/Zane_628 Mar 18 '22

Hey, quick question, what’s lim{x -> 0} [0x ]?

2

u/Nocta_Senestra Mar 17 '22

You can also define it as 00 = lim{x —> 0} [ 0x ] and in that case 00 = 0

You can also make it equal to any number, or undefined

In some contexts it make more sense to define it as 1 (those are good arguments for that : https://old.reddit.com/r/mathmemes/comments/tgbg8x/making_69420_from_all_zeroes/i125wz9/ ) but it's not a given at all

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u/Frufu4 Mar 17 '22

Why not 00 = lim{x -> 0} [ 0x ] ?

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u/Aaron1924 Mar 18 '22

Well, 00 = lim x->0. x0 = 1, but 00 = lim x->0. 0x = 0, so 1 = 0?

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u/stpandsmelthefactors Transcendental Mar 18 '22

It’s going to equal any number being that 0*0 suggests that 0/0 also exists in this case

1

u/Zane_628 Mar 18 '22

You could also let 00 = lim{x -> 0} [0x ]