The Warring States of NPF - "School Thread" or "Math + Seil = *headdesk*"

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- - "School Thread" or "Math + Seil = *headdesk*" (http://www.nuklearforums.com/showthread.php?t=37752)

It means congruent. It's like equals but stronger. Things that are congruent need not be strictly equal but things that are equal are always congruent. I plain English it's a bit like "the same as" or "similar to".

Edit: and I have no idea why it replaced some of the subtraction signs and the ' with question marks.

Quote:

It's like equals but stronger.

Wut?

Wait I said that backwards congruence is actually weaker than equals. It's an easy mistake to make. For example, take similarity and congruence from geometry. All congruent triangles are similar but not all similar triangles are congruent. Congruence is a stronger statement than similarity in geometry. Similarity means something like the same shape while congruent means same shape and size (i.e. it is more restrictive and therefore stronger). Likewise in modular arithmetic congruence is weaker because everything that is equal is also congruent but everything that is congruent is not equal. For all practical purposes you can treat congruence as equals in modular arithmetic.

It is showing up as three horizontal lines stacked on top of each other like an equals sign with an extra line right? Because that's how its supposed to look and I have no idea if it's in any sort of standard font package.

That is how it shows up, and you're the first person I've seen use congruent outside of the uni. I also like your taste in avatars, dimension-warping hobo.

Yeah, all that math stuff Sith just posted, the modular equations and all that? Just looking at it makes me want to go on a world-spanning quest to find the god-slaying sword and kill the spirit of math.

My ex was a math fine arts major and would like it was all numbers where NUMBERS SHOULDN'T BE. Occasionaly there would be a plus sign and I'd be like- I know what that does.

Quote:

Originally Posted by Sithdarth (Post 1034818)

Ok so here's a quick primer on modular (congruence) arithmetic. Basically it goes like this:
a ≡ b mod m ↔ a - b = k*m where a, b, m, and k are all integers.

So for example:
5 ≡ 2 mod 3
5 ≡ 1 ≡ -3 mod 4
5 ≡ -1 mod 6

Basically if a = q*m + r, 0 ≤ r ≤ (m-1) then a - r = q*m and a ≡ r mod m where r is called either the remainder or the least non-negative residue of a mod m.

Now there are some nice rules for modular arithmetic. For example, if a ≡ b mod m and c ≡ d mod m then:
a + c ≡ b + d mod m
a - c ≡ b - d mod m
a*c ≡ b*d mod m

Here are a few examples:
What is the remainder when 123*257*425 is divided by 7?
123 ≡ 4 mod 7
257 ≡ 5 mod 7
425 ≡ 5 mod 7

123*257*425 ≡ 4*5*5 = 100 ≡ 2 mod 7
So the remainder is 2.

What is the remainder of 37*77 when divided by 39?
37 ≡ 37 mod 39 and 37 ≡ -2 mod 39
77 ≡ 38 mod 39 and 38 ≡ -1 mod 39

37*77 = (-2)(-1) ≡ 2 mod 39
So the remainder is 2.

Just one more rule now:
If n > 0 and a ≡ b mod m then a^(n) ≡ b^(n) mod m
So for example:
What is the remainder when 2^(13) is divided by 33?

2^(5) ≡ 32 ≡ -1 mod 33
2^(13) = (2^(5))^2 * 2^(3) = (-1)^(2) * 8 ≡ 8 mod 33
So the remainder is 8.

Just for fun here is Little Fermat's Theorem:
Given a prime integer P two things must be true:

i) For any integer a, a^(P) ≡ a mod P
ii) If a is not a multiple of P then a^(P-1) ≡ 1 mod P

With this you have the mathematical foundation to understand RSA encryption which I'll write up later.

PS: That's only a small fraction of what I've learned about modular arithmetic this semester. There are ways to do pretty much all of the equation solving you do normally with modular arithmetic which can solve some pretty unusual problems. Then of course we moved into fractals. I'm contemplating back tracking a bit and showing you some of the spherical and hyperbolic geometry I did this semester too.

Look out guy, I think witchcraft may be bannable offense on this forum.

He's a witch! HE'S A WITCH!!!!

I use simple math for my daily life! Even work, all the crap math I learned through high school and college have become worthless to me and I have forgotten all it. All you need is addition, subtraction, multiplication and division. Oh and, NO ONE CARES WHEN THE TWO TRAINS WILL PASS EACH OTHER GOD DAMNIT! NO ONE!!!!

Quote:

Originally Posted by Sithdarth (Post 1034818)

schnip

That's pretty interesting actually, but don't you do physics? What part of physics is modular arithmetic needed for?

To Mr. Sithdarth, my rebuttal:

http://www.gdargaud.net/Humor/Pics/MathSucks.jpg

Quote:

Originally Posted by Unsynked

I can see the appeal of being able to make up an answer and still be correct, but the right/wrong division of logic is much more straightforward.

Woah, just saw this. It's not that I enjoy the fact that many answers can be right in Lit while in Math only one answer is right for one problem.

It's that most of my English profs. are really wacky guys, while me Math teacher is insane. Also, I can't wrap my head around numbers, but writing, reading, analyzing, critiquing... English just comes easier to me, alright?