Modular Arithmitic
You probably think you don't know what modular numbers are, but you do!
Modular arithmetic is also called clock arithmetic because it works exactly like a clock. On a clock instead of counting on to 13 after 12, you go back to 1. You know that 5 hours after 9 o'clock is going to be 2 o'clock not 14 o'clock. Only the numbers 1 to 12 exist.
Numbers that count around in circles like this are called modular numbers. The modulo or mod on a clock is 12. Every number can be expressed as a number between 1 and 12. But we are not limited to just 12, any positive integer can be a modulo.
In mod 6 we start counting at 1 again when we reach 6
Or sometimes it is considered 0, 1, 2, 3, 4, 5, 0, 1, 2 ... but really its the same thing
1, 2, 3, 4, 5, 6, 1, 2, 3 ...
Given a mod we are working in, any positive or negative integer can be converted into a number in that mod.
For example in mod 6
7≡1(mod 6)
8≡2(mod 6)
9≡3(mod 6)
The symbol that looks like and equals but has three lines means congruent or equivalent. So this notation tells us that in mod 6, 7 is equivalent to 1, 8 is equivalent to 2 and so on. It's actually quite a simple concept. But it does take some getting used to. Here are a couple sites to check out for more practice: Clock Arithmetic, Modular Art
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