We use modular arithmetic all the time. It's useful for situations where you want to start over, time being the most obvious. Say it's 9 o'clock. What time will it be 5 hours from now?

In modular arithmetic, when you get to the end of your finite list of numbers, you just loop back to the beginning, as if you were counting numbers around the face of a clock. For example, if you go ...

Keeping track of the game is an exercise in the useful arithmetic of remainders. ... This is known as arithmetic “modulo 12,” but we could use any number instead of 12.