# Thread: The meaning of [a]n(intersection of sets)[b]n...(proof)

1. ## The meaning of [a]n(intersection of sets)[b]n...(proof)

I dont know what this question is asking me.

It uses a symbol, an upside down U, apparently meaning intersection of sets. I have yet to deal with such an integers modulo n problem:

Let a and b be integers.

Prove that either [a]n(upside down U)[b]n = 0 or [a]n=[b]n

Note that the n's are subscripted. (congruence classes of modulo n)

2. Hello,

It would rather be $\displaystyle [a]_n \wedge [b]_n$ than $\displaystyle [a]_n \cap [b]_n$, wouldn't it ?

In this case, it would denote the gcd... but I don't see why it would equal 0.
So in which context is it ?

3. It is certainly the upside down U, Which the index decribes as intersection of sets. The other symbol is never mentioned. Also, the 0 is crossed off, if that is significant.[/COLOR][/COLOR]

4. Wouldnt this imply that [a]n and [b]n dont have any integers modulo n in common OR they have all of their integers modulo n in common?

5. The real question should be = empty set or [a]_n=[b]_n

When [a]_n \cap [b]_n =empty set, then [a]_n is not the same integer as [b]_n but when [a]_n \cap [b]_n has a value, then because [a]_n intersects with [b]_n at that point, then they are equal at that value.

6. Ahh yes, thats exactly what it means. How would the proof of this look?

7. Well you have a definition of intersection which is.. something along the lines of $\displaystyle [a]_n \cap [b]_n$ belongs to both [a]_n and [b]_n, right?

So [a]_n and [b]_n are integers. If $\displaystyle [a]_n \cap [b]_n$=empty set then [a]_n will not equal [b]_n. But if $\displaystyle [a]_n \cap [b]_n$= n such that n is some arbitrary integer, then out of necessity, [a]_n=n, and [b]_n=n which means [a]_n=[b]_n.

8. But that doesnt look like proof to me, it just looks like an explaination of the situation.

Can I get a second opinion?