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Math Help - The meaning of [a]n(intersection of sets)[b]n...(proof)

  1. #1
    Member elninio's Avatar
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    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)
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  2. #2
    Moo
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    Hello,

    It would rather be [a]_n \wedge [b]_n than [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 ?
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  3. #3
    Member elninio's Avatar
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    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]

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  4. #4
    Member elninio's Avatar
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    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?
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  5. #5
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    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.
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  6. #6
    Member elninio's Avatar
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    Ahh yes, thats exactly what it means. How would the proof of this look?
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  7. #7
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    Well you have a definition of intersection which is.. something along the lines of [a]_n \cap [b]_n belongs to both [a]_n and [b]_n, right?

    So [a]_n and [b]_n are integers. If [a]_n \cap [b]_n=empty set then [a]_n will not equal [b]_n. But if [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.
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  8. #8
    Member elninio's Avatar
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    But that doesnt look like proof to me, it just looks like an explaination of the situation.

    Can I get a second opinion?
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