Congruence/Modulo: https://en.wikipedia.org/wiki/Modular_arithmetic

Hi, I'm trying to understand modulo and congruence better and I really liked the wiki article - unfortunately he stops just short of intuitive-nirvana.

Basically that clock example is a bit incomplete. How would you express going from 7 to 3 on a clock as a congruence relationship? I think answering this question would help me understand the whole thing better but for the life of me, I can't seem to write it out.

Basically for the clock example on the Wiki, I want:

a congruent b (mod n)
(with numbers 7,3 filled in)
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He's talking about Equivalence Classes: where, two numbers 'x' and 'y' are equivalent for some equivalence relationship. In the clock example, 12 and 0 are equivalent for some k*n where k is Z (integers) and kn is the difference between 12 and 0. So I tried writing 12 == 0 (mod n) but that didn't make any sense *BOOHOO*

== is my symbol for congruence
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It gets really confusing in
https://en.wikipedia.org/wiki/Modular_arithmetic

The congruence relation may be rewritten as

a = k n + b ,
explicitly showing its relationship with Euclidean division. However, b need not be the remainder of the division of a by n
.

(edited 6 years ago)

Reply 1

veekm

15 congruent 3 (mod 12) is what he means by that clock example. He's basically saying 15hrs is equal to 3hrs - sheesh!