/sci/ - Science & Math

>>12303124
This comes from the same people who came up with Complex numbers.

>>12303124

your decimal counting system is a modulo.

>>12303156
I think that was Lionheart Oiler

>>12303165
you’re lying

>>12303180

assuming you are not trolling

you count in modulo 10, every 10 units you start again.
you use modulo 24 to count the hours of a day and modulo 360 to count a full rotation (angles).

I see no issues with moduli

>>12303124
>t. never had an linear algebra course

>>12303208
Or I could just count the hours of the day by saying 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

....?

>>12303166
for the lion heart

>>12303240
And what comes after hour 24?

The integers are a complicated structure. No matter how many integers you've counted, there will always be more. They are unending. Sometimes you have propositions that are supposed to hold for all integers and it's unclear how you would prove it without checking it for every single integer. Modular arithmetic helps with that. It massively reduces the amount of information and simplifies things. You will no longer have an infinite number of things, there are only finitely many classes mod n.
Let's say that you want to prove that given distinct list of 101 integers, two of them differ by a multiple of 100. At first it might sound like a complicated proposition. How would you prove that for any collection of integers? There are infinitely many such options, how do you even start? But then you notice you can work mod 100, where there are only 100 options. And two of the integers must correspond to the same option, which means exactly that their difference is a multiple of 100, so the problem is solved.
Another good example is considering integral solutions to polynomials. For example, how do you show that no integer x satisfies x^42 - 12x^40 + 4 =0? The task might seem daunting at first, but then you might try reducing the equation modulo 3. All you need is to check 3 cases: 0,1,2. If none of them are a solution, that means there's no integral solution. And indeed, it's easy to check that none of these work, so we have our proof.
Modular arithmetic is of course also useful for encryption. The ring Z/nZ is finite so operations that would be completely intractable in the integers like raising a number to a 2000 power become very feasible and this opens up many possibilities.
Taking note of facts about modular arithmetic also makes checking divisibility much easier. For example, to check that a number d_n d_(n-1) ... d_1 in base 10 is divisible by 11 just notice that 10=-1 mod 11 and so 10^n = (-1)^n which is very easy to calculate (-1 if n is odd and 1 if n is even).

>>12303254
So your number mod 10 just becomes d_1 - d_2 + d_3 - d_4. .... which is easily checked whether it's divisible by 11 or not.

>>12303240

and after 24 you restart, that's a modulo

>>12303260
>and after 24 you restart, that's a modulo
Yes, but is it numberwang?

>>12303124
to solve fizzbuzz with

>>12303208
You reuse the same numbers after 10 but it's not like the quantity changes. It's not like were gonna create a new symbol for each number. So is this a proper modulo? The true quantity doesn't reset but the numbers do because were not making infinite symbols.

>>12303287

well, not sure I totally get what you mean but I think it's correct, you could perfectly count in this way:

you draw a stick for every stone you see, you don't need a modulo but you will end up with a shitload of sticks and that's not convenient.

>>12303287
Modulo is an operator that allows you to describe any kind of cyclical behavior with math. Let's say you wanted to make a binary computer write out a number stored in its memory in base 10. How would you do it without modulo? You could come up with some convoluted and inefficient way of doing it but then you would just have come up with a more stupid way of writing what is, at its core, a modulo operation.

>>12303259
Poor monke

>>12303124
All modern computer hardware is limited to modular arithmetic for integer operations. Larger integers have to be implemented on top of it.

>>12303124
To answer when will you wake up, if you sleep for 8 hours starting at 22:00.

>>12303124
>It’s like nerds just make shit up to make things more difficult for themselves
are you trying to describe all of modern math?

>>12303124
mod is actually useful though. things in residue systems / certain rings have very good properties that we can actually do practical stuff with. The big poster child for this is cryptography. It shows up a lot in other parts of computer science.
More generally, if you understand modular arithmetic, it opens up a world of abstract algebra that can be pretty useful.

>>12303124
Aww, poor baby can't understand his CS homework. Modulo can be used for several things in modern computing. If you take a number x mod 2, you can find if x is even or odd. You can use modulo for keeping numbers within bounds for arithmetic (i.e. 12 hour clocks going from 12 to 1. AKA clocks are x mod 12). Modulo is the sole basis for encryption in modern computing.

I use it at my cuck factory job to make sure I didn't lose any parts because the last tray of pieces should have the proper remainder of the full total divided the quantity in each container. Can't even explain this to my dumbfuck coworkers how to use Mod on the calculator and they look at me funny. I hope they are all gassed to death by nazis,

>>12303124
Don't ever bother studying math or a math-adjacent field if you think a useful abstraction like that is "making things more difficult."

It's not even fucking hard, retard

>>12303124
It's very useful in computer science

>>12303448
this

>>12303165
This. Also, the reason why adding up the digits to see divisibility by three is because of modulo congruences in z mod n z. Pic related.

>>12303124
you can transform an infinite set to a finite one. Also cryptography uses it a lot, plus RNGs, hashing etc.

How the fuck is this thread still up???

>>12306173
Maybe because modulo is pointless to most normal people and only necessary for computers?