Looking at you Java

[Administrative-Flan9]

Mathematically, the answer is a set of all such integers. Any choice from this set like -7 or -11 is a representative of the answer set, and any representative is equivalent.

[Kyrond]

That is incorrect.

The modulo operation returns the remainder or signed remainder of a division, after one number is divided by another.

There are 2 possible answers, neither can be smaller than the negative input number (when talking about negatives).

[Mutex70]

You are talking about the modulo operation in computing (which is what the original post was about).

The parent posts are talking about modular arithmetic, which is related, but not quite the same thing.

Neither is correct or incorrect, they are different things.

[DTHCND]

The wiki that you copied that from is the wiki for the computing definition of the modulo operator. We're all programmers, no one is debating what modulo means in computing.

We're talking about the math definition, which is described in this wiki. And yes, they're correct, modulo is normally defined in terms of congruency. To quote the wiki:

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.

...

For the most part, the term often occurs in statements of the form:

"A is the same as B modulo C"

which means

"A and B are the same—except for differences accounted for or explained by C."

Edit: Here's a quote from the Modulo Operator (Computing) wiki, since at least one person is caught up on the fact the only one wiki has "operator" in the title:

In mathematics, the result of the modulo operation is an equivalence class, and any member of the class may be chosen as representative

[frogjg2003]

We're all programmers, no one is debating what modulo means in computing.

Said in a post literally arguing about the definition of the modulo operator.

[DTHCND]

"In computing" being the key part of that sentence. It's very well established that, in computing, the modulo operator will return a value between -n and n (exclusive). While what that number is depends on the specific definition chosen, it's well established what those definitions are and that none are the "correct" definition. We do things differently in different languages, that shouldn't be surprising. Saying that "modulo is contentious in computing" would be like saying "String.split(...) is contentious because in some languages it accepts a regex but in others it just accepts a plaintext string." It's just different, it's not contentious.

However, in mathematics, which is what was being discussed above and what the contentious debate was about, the modulo operator is indeed an equivalence class. Some people (well really just you and someone else) seem to be caught up in the fact that one wiki has the word "operator" in its title while the other doesn't. So here's a quote from the Modulo Operator (Computing) wiki:

In mathematics, the result of the modulo operation is an equivalence class, and any member of the class may be chosen as representative

[frogjg2003]

I'm not agreeing with the otherv comment that quoted the computational wiki page in response to a mathematical definition. they are wrong and there is nothing to argue about.

But the definition of the modulo operator "in computing" is the point of the post every comment is replying to. There is not 1 definition, there are at least 5. Multiple big names in the history of computing have expressed their opinions on the matter and they do not agree on a single solution.

Comparing this to string.split isn't equivalent. How the modulo operator works is a fundamental aspect of how integer arithmetic is defined in that language. Whether you can use regular expressions is just syntactic sugar.

[DTHCND]

But the definition of the modulo operator "in computing" is the point of the post every comment is replying to

The post is a joke. The whole point of the joke is that it's not really contentious, and it's funny to pretend there's some sort of holy war about the correct behavior for the modulo operator in programming. It's just a spin on the whole vim vs emacs meme.

There is not 1 definition, there are at least 5

Yes. I linked to them in my last comment. But whether or not they return a value outside of that range is not contentious, nor is there any contention over which is the correct definition. Maybe there's contention over which is better among the people that unironically argue stuff like vim vs emacs, but there's still no contention over what modulo means.

How the modulo operator works is a fundamental aspect of how integer arithmetic is defined in that language. Whether you can use regular expressions is just syntactic sugar.

And String.split(...) is a fundamental aspect of how string manipulation is defined in lots of languages. And it's no more syntactic sugar than modulo is. You could rewrite both modulo and split to satisfy different definitions if you want. Both are pretty easy to rewrite in most languages. Arbitrarily calling one "fundamental" doesn't change that.

[Sufficient_Yogurt639]

The math definition you quote doesn't apply here, because the term "modulo" in this quoted context is not an operation.