Why_must_H_be_normal?
motivates the article
What modular arithmetic does to the set of integers
What’s the remainder of 6 when its divided by 5? one! What’s the remainder of 10 when divided by 5 zero You’ve probably encouterd modular arithmetic which is a formal way of asking what’s the remainder of number a when its divided by. Formally we defined it as a is congruent to b mod 5 where b is a the remainder.this is true wehn a-b is divisible by 5. What’s the remainder of -1 when its divided by 5? Our human intuitiion of divivision breaks when it comes to negative numbers. Hopefully the defintiion of of modular arithmetic can grants us the answer to this questions. We ask ourselve, what’s the the remainder b such that when we do -1-b we have a number divisible by 5 or a mutliple of 5 if you prefer? Try it! leave space here for answer! One possible answer is 4 since -5 is a multiple of 5. If We go one intgers after the other and ask what’s the smallest number b such we subtract that integers b from you we get a multiple of five. and depending on the answer we place each integerts in a group. Then we get those 5 groups below Here I will write latex and some elements of those groups and … notation on both sides to see they are infinite