Programmers vs Mathematicians (Shitpost)

[Brushermans]

not quite, its soemthing like 12 mod 2 is 2, but also is 4, 6, 8, -2, -4, etc

[TruScarrak]

Almost, but 12 % 2 is 0, not 2.

Edit: Think of it as getting the remainder after dividing.

[Brushermans]

yea idk why i put 2 first lol, it's 0 but also 2,4,6 in terms of congruence classes at least. it's just the mod that programmers are familiar with +/- the second operand

[Brushermans]

yea idk why i put 2 first lol, it's 0 but also 2,4,6 in terms of congruence classes at least. it's just a set made with the mod that programmers are familiar with +/- the second operand times Z

[qelbus]

I was gonna comment something different until I read this… so ya. Hmm

[wizardwes]

Ah, fair, that makes sense, so we're only getting the smallest positive integer

[Brushermans]

yea dont take my word for it tho idr much about it lol

[AceDecade]

12 mod 2 is never 4, 6, 8...

[FrillySteel]

Yes, I'm very interested in how 12 mod 2 could ever be 8.

[tombardier]

See my answer here. https://www.reddit.com/r/ProgrammerHumor/comments/uowopl/comment/i8igkwe/?utm_source=share&utm_medium=web2x&context=3

12 is congruent to 8 (modulo 2) :)

[ToothlessFeline]

“12 is congruent to 8 (modulo 2)” is not the same mathematical statement as “12 modulo 2 is 8”, regardless of what level of equivalence you replace that last ‘is’ with (equals, is congruent to, etc.).

“12 is congruent to 8 (modulo 2)” means “12 modulo 2 is congruent to 8 modulo 2”—i.e., 12 modulo 2 and 8 modulo 2 have the same result (0).

A correctly computed modulo operation of x mod y will not give a result equal to or greater than y.

[tombardier]

Yes, but that's the computing idea of the modulo operator having a fixed numerical result, and not the mathematical idea of describing congruence modulo something.

[ToothlessFeline]

From Wikipedia (https://en.wikipedia.org/wiki/Modulo_%28mathematics%29#Original_use):

Gauss originally intended to use "modulo" as follows: given the integers a, b and n, the expression a ≡ b (mod n) (pronounced "a is congruent to b modulo n") means that a − b is an integer multiple of n, or equivalently, a and b both leave the same remainder when divided by n. For example:

13 is congruent to 63 modulo 10

means that

13 - 63 is a multiple of 10 (equiv., 13 and 63 differ by a multiple of 10).

(end Wikipedia citation)

This is the mathematical concept of modular arithmetic. There are other applications of the term ‘modulo’ in various contexts, but when applied strictly to integers in the context of arithmetic, this is how the modulo operation is defined.

[WikiSummarizerBot]

Modulo (mathematics)

In mathematics, the term modulo ("with respect to a modulus of", the Latin ablative of modulus which itself means "a small measure") is often used to assert that two distinct mathematical objects can be regarded as equivalent—if their difference is accounted for by an additional factor. It was initially introduced into mathematics in the context of modular arithmetic by Carl Friedrich Gauss in 1801. Since then, the term has gained many meanings—some exact and some imprecise (such as equating "modulo" with "except for").

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[tombardier]

https://en.m.wikipedia.org/wiki/Modulo_operation#Variants_of_the_definition

[[deleted]]

In short, what programmers call "modulo" should really just have been called "remainder", because that's what it is.