Livefyre Profile

Activity Stream

Sorry, goat. Don't scroll down. 

1 day, 12 hours ago on Dodgers 7, Padres 1: Finally Some Offense

Reply

@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. 

1 day, 12 hours ago on Dodgers 7, Padres 1: Finally Some Offense

Reply

@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. 

1 day, 12 hours ago on Dodgers 7, Padres 1: Finally Some Offense

Reply

@OCDodger Some could argue the same, even. 

1 day, 12 hours ago on Dodgers 7, Padres 1: Finally Some Offense

Reply

@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. 

1 day, 12 hours ago on Dodgers 7, Padres 1: Finally Some Offense

Reply

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

1 day, 12 hours ago on Dodgers 7, Padres 1: Finally Some Offense

Reply

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

1 day, 12 hours ago on Dodgers 7, Padres 1: Finally Some Offense

Reply

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

1 day, 12 hours ago on Dodgers 7, Padres 1: Finally Some Offense

Reply

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

1 day, 12 hours ago on Dodgers 7, Padres 1: Finally Some Offense

Reply

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

1 day, 12 hours ago on Dodgers 7, Padres 1: Finally Some Offense

Reply

@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. 

1 day, 12 hours ago on Dodgers 7, Padres 1: Finally Some Offense

Reply

@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 kZ/n or [k]_n

1 day, 12 hours ago on Dodgers 7, Padres 1: Finally Some Offense

Reply

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

1 day, 12 hours ago on Dodgers 7, Padres 1: Finally Some Offense

Reply

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

1 day, 12 hours ago on Dodgers 7, Padres 1: Finally Some Offense

Reply

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

1 day, 12 hours ago on Dodgers 7, Padres 1: Finally Some Offense

Reply

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

1 day, 12 hours ago on Dodgers 7, Padres 1: Finally Some Offense

Reply

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

1 day, 12 hours ago on Dodgers 7, Padres 1: Finally Some Offense

Reply

joyful game was joyful. 

1 day, 12 hours ago on Dodgers 7, Padres 1: Finally Some Offense

Reply

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

1 day, 12 hours ago on Dodgers 7, Padres 1: Finally Some Offense

Reply

(Shhh, I'm not really here)

2 days, 6 hours ago on Dodgers @ Padres Aug. 31, 2014: Welcome back Ryu and Uribe

Reply

We finally scored a bunch of runs with bases loaded.

2 days, 6 hours ago on Dodgers @ Padres Aug. 31, 2014: Welcome back Ryu and Uribe

Reply

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

2 days, 6 hours ago on Dodgers @ Padres Aug. 31, 2014: Welcome back Ryu and Uribe

Reply

@BIah having issues with internet. i was here earlier too

2 days, 7 hours ago on Dodgers @ Padres Aug. 31, 2014: Welcome back Ryu and Uribe

Reply

that's frustrating 

2 days, 8 hours ago on Dodgers @ Padres Aug. 31, 2014: Welcome back Ryu and Uribe

Reply

it's good to see van slyke playing again

2 days, 8 hours ago on Dodgers @ Padres Aug. 31, 2014: Welcome back Ryu and Uribe

Reply

okay, bai

5 days, 13 hours ago on Alex Guerrero Is Heating Up At The Right Time

Reply

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

5 days, 13 hours ago on Alex Guerrero Is Heating Up At The Right Time

Reply