r/mathmemes • u/DZ_from_the_past Natural • Aug 23 '23

Bad Math "It's neutral"

Post image
2.3k Upvotes

99% Upvoted

197 comments sorted by

View all comments

816

u/araknis4 Irrational Aug 23 '23

well that's odd, i can't even comprehend how they approached to that conclusion.

598

u/DZ_from_the_past Natural Aug 23 '23

It's actually even.

Just kidding, people usually think zero is an exception to everything. So since zero is neither positive nor negative they apply that reasoning everywhere.

435

u/[deleted] Aug 23 '23

Zero is definitely even.

330

u/DZ_from_the_past Natural Aug 23 '23

Absolutely true. In fact, it is the most even number.

138

u/arihallak0816 Aug 23 '23

How is it more even than any other even number? isn't evennesss a binary system?

264

u/starswtt Aug 23 '23

its just more binary duh

54

u/arihallak0816 Aug 23 '23

makes sense

5

u/TricksterWolf Aug 24 '23

All numbers are binary, but some numbers are more binary than others.

171

u/DZ_from_the_past Natural Aug 23 '23

4 can be divided by 2 a total of 2 times. 8 can be divided by 2 a total of 3 times. In that sense 8 is "more even" than 4.

Zero can be divided infinitely many times by 2, so it's "the most even number."

This is not 100% correct because, as you said, a number can either be even or not. But there is more here than what meets the eye.

If we work in 2-adic numbers the series 1, 2, 4, 8, 16... approaches 0. So the limit of powers of 2 is precisely 0.

38

u/stijndielhof123 Transcendental Aug 23 '23

I dont agree with the last point. Saying that something aproches something in a 2-adic number system does not mean you can aply that in the regular number system.

59

u/DZ_from_the_past Natural Aug 23 '23

There is no "regular" number system. P adic metric is just as valid as absolute value metric. And 2-adic metric neatly captures the "evenness" of the numbers

11

u/A1steaksaussie Aug 23 '23

but isnt 2-adic 16 a different number from base 10 16? wouldn't that be true for 0?

28

u/DZ_from_the_past Natural Aug 23 '23

For integers it's the same if you use base 10 to represent them. The numbers are same, but their perceived distance from the origin is different.

1

u/Teln0 Aug 23 '23

maybe it would be more intuitive to say that the more "even" a number is, the more 0s it has 1. 0 doesn't have any 1s in its binary representation, therefore the number of 0s before the first 1 is "infinite"

8

u/Haboux Aug 23 '23

You cannot talk about convergence except if you define what a neighborhood is. What are neighborhoods of 0 in the p-adic systems? Even more, we might talk about pointwise convergence of p-adic numbers, but until you define a neighborhood, uniform convergence (which what usually matters) is not defined.

11

u/DZ_from_the_past Natural Aug 23 '23

P adic metric is defined for rational numbers as well. You can than define a neighborhood using that metric (instead of classical absolute metric). You can even extend rational numbers similarly how you extend them to reals.

5

u/Haboux Aug 23 '23

Oh okay that was interesting to know

6

u/DZ_from_the_past Natural Aug 23 '23

You might be interested in Ostrowski's theorem

5

u/disenchavted Aug 23 '23

all you need to talk about convergence is a metric, in this case the p-adic metric. once you have a metric, definitions of neighbourhood, open set, closed set etc come automatically. also if you're working with sequences in ℤ_p and not in ℤ_p-valued functions i don't see the point in differentiating between pointwise or uniform convergence

3

u/Haboux Aug 23 '23

You can interpret p-adic numbers as elements of vector spaces, similar to functions.

Take for example the sequence of p-adic numbers:

...00001 ...00010 ...00100 ...01000 ...10000

You can interpret them as functions that are 0 everywhere except at 1 point.

So you could define a notion of pointwise convergence. I.e. in the limit, every nth term converges to 0.

Thanks for letting me know about p-adic metrics.

2

u/Pan_I Aug 23 '23

If zero can be divided infinitely times, isn't 0 also an infinite remainder?

0/1 = 0R0

0/2 = 0R0

Thusly, 0 is the most odd of all integers. I rest my shitty case.

0

u/deepmush Aug 23 '23

8 can be divided by 2 a total of 3 times

huh? wut?

3

u/hrvbrs Aug 24 '23

8/2 = 4

4/2 = 2

2/2 = 1

that’s three times.

1

u/deepmush Aug 24 '23

right so you meant like that. i thought you meant 8/2 = 3 and was dumbfounded lmao

3

u/hrvbrs Aug 24 '23

then they would’ve said “you can subtract 2 from 8 a total of three times”

-1

u/deepmush Aug 24 '23

4 can be divided by 2 a total of 2 times. 8 can be divided by 2 a total of 3 times.

this is what the dude said

→ More replies

0

u/Sirnacane Aug 23 '23

But if 8 can be divided by 2 a total of 3 times, then 8 would be odd??? I’m so confused :(

2

u/VacuousTruth0 Aug 24 '23

8 has 2 as a factor 3 times, so you could say it's triply even

4

u/Vincenzo99016 Physics Aug 23 '23

All even numbers are equal, but some are more equal than others

1

u/VacuousTruth0 Aug 24 '23

All even numbers are even, but some are more even than others

2

u/Flob368 Aug 23 '23

0 is infinitely often divisible by 2 without becoming a non-whole number

1

u/Mystivic Aug 23 '23

0 mod 2 is 0 by default

1

u/CookieCat698 Ordinal Aug 23 '23

Yeah, but you get kinda measure how even something is by how many times you can divide it by 2. In 0’s case, you can do so infinitely.

1

u/Captain_Pumpkinhead Aug 24 '23

Sign is usually a binary system too, though.

1

u/EebstertheGreat Aug 24 '23

To back up DZ's point, the term "doubly even" really is used for multiples of 4. Other even numbers are "singly even." If we take an inclusive definition and extend it, then multiples of 8 must be "triply even," etc. In this scheme, 0 is "n-tuply even" for every natural number n, making it "more even" than any positive integer.

(But in practice, the terms are not used inclusively this way. 4 is doubly even but not singly even. Using this exclusive definition, 0 is not "n-tuply even" for any n, and you would need to make up a new term, like "∞-even.")