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Maths Question

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    Stuck on the last part, if anybody could help would be great,

    Thanks.
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    (Original post by Reety)


    Stuck on the last part, if anybody could help would be great,

    Thanks.
    Consider [1]. What is this set?
    Consider [2]. What is this set?
    There intersection is...?
    Hence the infinite intersection is...?
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    (Original post by Reety)
    1 is all odd numbers and 2 is all the even?
    Well 1 is not all odd numbers. It's all numbers that differ from 1 by a multiple of 4, as per the definition of the relation.

    So, [1]=\{...,-7,-3,1,5,9,13,...\}


    What do you mean hence the infinite intersection? like [4+i] or [i-4]?
    [0]\cap[1]\cap[2]\cap[3]\cap...\cap[n]

    Edit: Your post has gone. I presume you've resolved it then.
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    (Original post by ghostwalker)
    Well 1 is not all odd numbers. It's all numbers that differ from 1 by a multiple of 4, as per the definition of the relation.

    So, [1]=\{...,-7,-3,1,5,9,13,...\}




    [0]\cap[1]\cap[2]\cap[3]\cap...\cap[n]

    Edit: Your post has gone. I presume you've resolved it then.
    my post was gone because i didn't even know if was making sense myself lul.. im so stuck

    so would i write that last question as what you have written:
    [0]\cap[1]\cap[2]\cap[3]\cap...\cap[n]
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    (Original post by Reety)
    my post was gone because i didn't even know if was making sense myself lul.. im so stuck

    so would i write that last question as what you have written:
    [0]\cap[1]\cap[2]\cap[3]\cap...\cap[n]
    That is what the question is asking (though not the answer), as n goes off to infinity.

    In practice we note that [0] = [4], etc, and there are only 4 sets.

    The notation  \displaystyle \bigcap_{i=1}^{\infty}, is similar to the sigma notation, except we're dealing with intersection of sets, rather than adding numbers.
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    (Original post by ghostwalker)
    That is what the question is asking (though not the answer), as n goes off to infinity.

    In practice we note that [0] = [4], etc, and there are only 4 sets.

    The notation  \displaystyle \bigcap_{i=1}^{\infty}, is similar to the sigma notation, except we're dealing with intersection of sets, rather than adding numbers.
    right, i get what you're saying about [0] = [4]... ,

    But how would I simplify that into an answer, I've been clueless for ages.
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    (Original post by Reety)
    right, i get what you're saying about [0] = [4]... ,

    But how would I simplify that into an answer, I've been clueless for ages.
    Go back to my first reply, What's [1]n[2]? as a set? What elements, if any, are in it?
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    (Original post by ghostwalker)
    Go back to my first reply, What's [1]n[2]? as a set? What elements, if any, are in it?
    [1] = 4n + 1 (where n is any integer).
    [2] = 4n + 2

    so they don't intersect?
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    (Original post by Reety)
    [1] = 4n + 1 (where n is any integer).
    [2] = 4n + 2

    so they don't intersect?
    Correct.

    So, the intersection of the two is the empty set. If you now intersect that with anything else, even an infinite number of anythng elses, it will still be the empty set.
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    (Original post by ghostwalker)
    Correct.

    So, the intersection of the two is the empty set. If you now intersect that with anything else, even an infinite number of anythng elses, it will still be the empty set.
    mhm.. right.. so how would i write that?

    is that the answer to the last part then?
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    (Original post by Reety)
    mhm.. right.. so how would i write that?
    You can list a set by its elements, { } in this case as it doesn't have any, or use the standard symbol for an empty set of, \emptyset

    Yes, that's the answer to the last part.
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    Is that the answer then:  \displaystyle \bigcap_{i=1}^{\infty} = \emptyset n [0] n [1] n [2] n [3]
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    (Original post by Reety)
    Is that the answer then:  \displaystyle \bigcap_{i=1}^{\infty} = \emptyset n [0] n [1] n [2] n [3]
    Not quite:

     \displaystyle \bigcap_{i=1}^{\infty} [i] = \emptyset
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    (Original post by ghostwalker)
    Not quite:

     \displaystyle \bigcap_{i=1}^{\infty} [i] = \emptyset
    Thank you very much!
 
 
 
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