@Tymathee @Tired Math Cat he hates math

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Sorry, goat. Don't scroll down.

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@Lobo @Tired Math Cat @OCDodger see what I said earlier. Good programming is very similar to an elegant proof. It requires the same kind of thinking.

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@OCDodger You use these equivalence classes everyday. Look at a clock. Americans "restart" the clock every 12 hours, and denote it by am or pm. Let's consider this in 24 hour time. Midnight is 0, noon is 12, 1:00pm is 13, etc. With all whole numbers between 0 and 24, 0, 12, and 24 are the only three that are divisible by 12. Every other number has a remainder.

Real quick reminder:

dividend ÷ divisor = quotient. Here, our divisor is 12.

If you divide the numbers (say x) between 0 and 12 (0 < x < 12) by 12, the quotient is 0, and the remainder is the dividend (x). Namely,

1 / 12 = 0 with remainder 1

2 / 12 = 0 with remainder 2

8 / 12 = 0 with remainder 8

But let's consider the numbers (again, x) between 12 and 24. (12 < x < 24). Then the quotient is 1 and the remainder is just difference between the dividend and 12. For instance,

13 / 12 = 1 with remainder 1 and 13 - 12 = 1

14 / 12 = 1 with remainder 2 and 14 - 12 = 2.

20 / 12 = 1 with remainder 8 and 20 - 12 = 8.

Let's say we had 36 hours in a day. Then for 1 am is 25 hours, 2 am is 26 hours, 8 am is 32 hours, etc. Further,

25 / 12 = 2 with remainder 1 and 25 - (12*2) = 1.

26 / 12 = 2 with remainder 2 and 26 - (12*2) = 2.

32 / 12 = 2 with remainder 8 and 32 - (12*2) = 8.

So instead of doing this over and over again, we can just write [1]_12 to say "all numbers with remainder 1 when divided by 12," or more concisely, "class 1 **mod** 12." (Same modulus you deal with in programming.) So,

[1]_12 = {1, 13, 25, 37, ... }

[2]_12 = {2, 14, 26, 38, ... }

[8]_12 = {8, 20, 32, 50, ... }

and

[0]_12 = {0, 12, 24, 36, 48, ... }

So there are a finite number of classes, exactly 12 for our example. And yet, we're able to represent every integer within these classes. A finite way to write infinitely many integers. Blew my mind.

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@nsxtasy @Tired Math Cat @OCDodger I did not!

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@OCDodger @Tired Math Cat it might've been out of the way for your CS requirements, but that class would've helped with algorithmic thinking. For some reason, the mathematics world uses real analysis as a stepping stone after discrete mathematics for formal proof writing. Good programming is similar to an elegant proof.

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@OCDodger @Tired Math Cat now that's silly, because you definitely will.

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@Tymathee @Tired Math Cat @Mike Petriello and people say we aren't welcoming. ha

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@OCDodger @Tired Math Cat Sorry, I was more geeking out in memory than explaining.

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@Tymathee @Mike Petriello doesn't matter who, just *someone*

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@Tymathee @Mike Petriello the goal is always to piss someone off.

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@OCDodger and then it turns out that's what we're doing with real numbers too. I seriously underestimated how interesting real analysis was going to be. I shouldn't have taken it last.

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@OCDodger @Tired Math Cat Oh my goodness, abstract algebra was so much fun. I took it right after intro to number theory, which was pretty easy. But the way my abstract algebra professor described equivalence classes blew my mind. A finite representation of countably infinite numbers. Just by writing k**Z**/n or [k]_n

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@OCDodger @Tired Math Cat oh i read what I wanted to read. I thought you said you majored in math. completely ignored the wish

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@OCDodger @Tired Math Cat but yes, very.

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@OCDodger @Tired Math Cat i consider CS the first derivative of mathematics.

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@OCDodger @Tired Math Cat you heard pure math is pretty ridiculous or you know it is? i love it. I absolutely love it.

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@OCDodger @Tired Math Cat This is wonderful if true. That means we have 4 math people (including brim)

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I heard matty's slide on the radio. The gif is great.

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@OCDodger @Tired Math Cat O'RLY

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@Mike Petriello lol

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joyful game was joyful.

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WE DID IT! WE WON! WE SCORED RUNS WITH BASES LOADED! IT WAS WONDERFUL!

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(Shhh, I'm not really here)

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We finally scored a bunch of runs with bases loaded.

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Finally

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okay guys, it's on you to make sure we win. family enjoys spending time together, for some reason

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way to go kemp

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aha!

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test?

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@Disgruntled Goat @Tired Math Cat freaking loaded, mang

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that's frustrating

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it's good to see van slyke playing again

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hi

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@Matt Kemp's Bath Towel @DBrim @Tired Math Cat and always it is

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@Matt Kemp's Bath Towel @DBrim @Tired Math Cat he could've been multitasking.

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@Ring-TailedBlehmur efb?

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new?

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That was shitty.

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okay, bai

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@i attend the AVNs i'm joking

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I completely forgot about his ear being ripped off. That's totally going to mess with his balance.

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