What is the benefit of modular mathematics? And is this correct?

$ \color{Black}{\Rightarrow mod(3,2) = 1 }$

Question

What is the benefit of modular mathematics? And is this correct?

$ \color{Black}{\Rightarrow mod(3,2) = 1 }$

anonymous · Answer

Modular arithmetic is used a lot in quite a few areas, from number theory to abstract algebra. And yes, 3 mod 2 is 1. Basically, the modulus function returns the remainder upon division.

parthkohli · Answer

Yes, but can you give me an example of a question based on modular arithmetic?

anonymous · Answer

Well for example in abstract algebra we study the groups of the form $\mathbb Z/n\mathbb Z$, which are modular groups of integers, and we find that in many cases all groups of a given order are isomorphic to a modular integer group. This is always true when n is prime, for example. Hard to explain that better without covering a lot of definitions from group theory.

parthkohli · Answer

And can you tell me what is clock 12....or something like that? (cant recall what that was called)

anonymous · Answer

Well a clock is a common example of modular arithmetic, mod 12. Because if it's 11:00, two hours later it will be 1:00, that is like 11+2 in mod 12.

parthkohli · Answer

I see. Thanks!