# OKay, what is a mod ?

1. Oct 4, 2011

### flyingpig

OKay, what is a "mod"...?

1. The problem statement, all variables and given/known data

Verify the proposition
[PLAIN]http://img442.imageshack.us/img442/7808/unledah.png [Broken]

3. The attempt at a solution

I don't know how to start, all I see is that 0/m belongs to Z...

Last edited by a moderator: May 5, 2017
2. Oct 4, 2011

### Staff: Mentor

Re: OKay, what is a "mod"...?

Surely wikipedia can offer some help, right? Don't waste our time on trivial questions that you can easily answer for yourself.

3. Oct 4, 2011

### DaveC426913

Re: OKay, what is a "mod"...?

I'm not sure that wiki will help him solve this. Yes, he might learn what mod means, but he said he doesn't know where to start. Surely he could use a shove in the right direction.

4. Oct 4, 2011

### SammyS

Staff Emeritus
Re: OKay, what is a "mod"...?

If (b-a)/m ∊ , that means b-a is an integer multiply of m, i.e. (b-a)/m has a remainder of zero.

5. Oct 4, 2011

### Staff: Mentor

Re: OKay, what is a "mod"...?

It would probably help him answer the question in his thread title.

6. Oct 4, 2011

### SammyS

Staff Emeritus
Re: OKay, what is a "mod"...?

Yes, what Mark said sounded rather harsh, but Mark & I & several others (even micromass worked with him though a multi-page thread recently) have a fairly extensive history of working with fp (flyingpig), so Mark knows him fairly well, and had his reasons for that post.

I'm sure Mark didn't intend for that remark to be mean-spirited.

7. Oct 4, 2011

### DaveC426913

Re: OKay, what is a "mod"...?

Yes, but you didn't finish reading his post before spewing venom.

8. Oct 4, 2011

### flyingpig

Re: OKay, what is a "mod"...?

Okay all that

"congruent module" (big words) mean is that some number m beside the "mod" means whatever comes in front is a divisor, nothing more than that.

Jesus these unnecessary abstract words are killing me

Sorry for causing the ruckus.

What exactly is there to verify? As Sammy said there is no reminder (0? )

aRb = bRa

9. Oct 4, 2011

### uart

Re: OKay, what is a "mod"...?

The question gives you the definition of "modulo equals" and then asks you to (use that definition to) verify that it's an equivalence relation.

For example, Show that if "a=b mod m" and "b=c mod m" that "a=c mod m" and so on.

10. Oct 5, 2011

### Staff: Mentor

Re: OKay, what is a "mod"...?

Right, I didn't. "Peeved" is closer to what I was feeling. In retrospect I should have toned what I said down a notch or so.

No, Dave, I did read his entire post, which also includes, "I don't know how to start..." My intent was to get flyingpig to do due diligence by looking up some basic terminology.

11. Oct 5, 2011

### flyingpig

Re: OKay, what is a "mod"...?

COuld someone please critique my work?

12. Oct 5, 2011

### flyingpig

Re: OKay, what is a "mod"...?

I just want to correct one small thing in the problem. It actually asks me to PROVE and not VERIFY, though I don't think there is a difference in this case.

13. Oct 5, 2011

### Staff: Mentor

Re: OKay, what is a "mod"...?

Your work in post #8 looks OK at a quick glance, but your book's definition of modulo requires me to do mental translation, and your use of m and M makes it more difficult to follow than it needs to be.

a $\equiv$ b (mod m) is usually defined to mean that a - b = km for some integer k.

Modulo arithmetic divides the integers into equivalence classes based on their remainders when divided by m.

For example, in modulo 7, the only possible remainders are 0 (multiples of 7), 1, 2, 3, 4, 5, and 6.

13 $\equiv$ 6 (mod 7), because 13 - 6 = 7 = 1*7.

14. Oct 5, 2011

### flyingpig

Re: OKay, what is a "mod"...?

So it's just my poor choice of letters that's really wrong because I was worried about transitivity part ? It's not my book it's my notes our prof sent to us lol

15. Oct 5, 2011

### SammyS

Staff Emeritus
Re: OKay, what is a "mod"...?

See red inserts.
And finally, ... Why did you put in a quote what wasn't in a post anywhere? Makes it difficult for others to include that stuff in a quote.

Had to CUT & PASTE it.

16. Oct 5, 2011

### icystrike

Re: OKay, what is a "mod"...?

Let me give you a loose defn of "mod"

If a=b+km
s.t k is an integer,

a==b (mod m)

17. Oct 5, 2011

### flyingpig

Re: OKay, what is a "mod"...?

LOl, I actually did it because I thought it would look neat. I had no idea it would be the other way around. Reminds me of that time I had so many spoilers no one (HallsofIvy, you, and someone else, I think it was vela) knew what on earth I was doing

What's wrong with saying "$$a \equiv b$$ is divisible by m"?

18. Oct 5, 2011

### SammyS

Staff Emeritus
Re: OKay, what is a "mod"...?

Well, I just had to give you some crap about that "QUOTE" thing. I did make you post look nice, and the cutting & pasting wasn't really that difficult.

19. Oct 5, 2011

### diligence

Re: OKay, what is a "mod"...?

I sympathize with struggling with terminology, but not every abstract concept has an explanation as succinct as this. If math was structured the way you propose, with no terminology beyond the basic stuff, most advanced concepts would require a tangled mess of implications to explain, and textbooks and research papers would require A TON more paper. It would always have to go back to the basic axioms, which would obviously be completely ridiculous.

As Sammy said, the are certainly NOT unnecessary