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Thread: Sets: Given 𝑨 = {𝒏 ∈ ℤ|1 ≤ 𝒏 ≤ 𝟏0}, define 𝑨𝒎 = {𝑛 ∈ 𝐴|𝑛 𝑖𝑠 factor of 𝑚}

  1. #1

    Sets: Given 𝑨 = {𝒏 ∈ ℤ|1 ≤ 𝒏 ≤ 𝟏0}, define 𝑨𝒎 = {𝑛 ∈ 𝐴|𝑛 𝑖𝑠 factor of 𝑚}

    Hi,

    can someone help me with understanding this:

    Let 𝑨 = {𝒏 ∈ ℤ|1 ≤ 𝒏 ≤ 𝟏0}.
    For any positive integer 𝒎 we define the set 𝑨𝒎 by𝐴𝑚 = {𝑛 ∈ 𝐴|𝑛 𝑖𝑠 factor of 𝑚}

    So I created set A = {-infinite,...,-1,0,1,2,...,10}
    But I'm stuck with Am.

    Is this right solution?

    A1 = {1}
    A2 = {1,2}
    A3 = {1,2,3}
    ...
    ?
    Thanks

  2. #2
    Elite Member stapel's Avatar
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    Cool

    Quote Originally Posted by kironet View Post
    Let 𝑨 = {𝒏 ∈ ℤ|1 ≤ 𝒏 ≤ 𝟏0}.
    For any positive integer 𝒎 we define the set 𝑨𝒎 by𝐴𝑚 = {𝑛 ∈ 𝐴|𝑛 𝑖𝑠 factor of 𝑚}

    So I created set A = {-infinite,...,-1,0,1,2,...,10}
    But I'm stuck with Am.

    Is this right solution?

    A1 = {1}
    A2 = {1,2}
    A3 = {1,2,3}
    ...
    ?
    I dunno. What did they tell you to do with "A" and "Am"? Are you supposed to list out the elements of all such sets "Am"? Or something else?

    Thank you!

  3. #3
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    Quote Originally Posted by kironet View Post
    Hi,

    can someone help me with understanding this:

    Let 𝑨 = {𝒏 ∈ ℤ|1 ≤ 𝒏 ≤ 𝟏0}.
    For any positive integer 𝒎 we define the set 𝑨𝒎 by𝐴𝑚 = {𝑛 ∈ 𝐴|𝑛 𝑖𝑠 factor of 𝑚}

    So I created set A = {-infinite,...,-1,0,1,2,...,10}
    But I'm stuck with Am.

    Is this right solution?

    A1 = {1}
    A2 = {1,2}
    A3 = {1,2,3}
    ...
    ?
    Thanks
    Your "A" is wrong; you seem to have missed that 1 ≤ n.

    If you were told to write out the first several sets Am, when you say that A3 = {1,2,3}, you are saying that 1, 2, and 3 are all factors of 3 (since m is 3, and you need to list every element of A that is a factor of m). Is that right?

  4. #4
    Hi, sorry this is the full question:

    Let 𝑨 = {𝒏 ∈ ℤ|1 ≤ 𝒏 ≤ 𝟏0}.
    For any positive integer 𝒎 we define the set 𝑨𝒎 by𝐴𝑚 = {𝑛 ∈ 𝐴|𝑛 𝑖𝑠 factor of 𝑚}

    Give the sets 𝐴3, 𝐴6 and 𝐴8 explicitly in terms of their elements.

    After research I came up with this:

    A = {1,2,...,10}
    A3={1,3}
    A6={1,2,3,6}
    A8={1,2,4,8}

    Does it look correct?
    Last edited by kironet; 02-03-2018 at 08:45 PM.

  5. #5
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    Quote Originally Posted by kironet View Post
    Hi, sorry this is the full question:

    Let 𝑨 = {𝒏 ∈ ℤ|1 ≤ 𝒏 ≤ 𝟏0}.
    For any positive integer 𝒎 we define the set 𝑨𝒎 by𝐴𝑚 = {𝑛 ∈ 𝐴|𝑛 𝑖𝑠 factor of 𝑚}

    Give the sets 𝐴3, 𝐴6 and 𝐴8 explicitly in terms of their elements.

    After research I came up with this:

    A = {1,2,...,10}
    A3={1,3}
    A6={1,2,3,6}
    A8={1,2,4,8}

    Does it look correct?
    Well, let's check it:

    A = {1,2,...,10} -- these are the numbers such that 1 ≤ 𝒏 ≤ 𝟏0 -- yes
    A3={1,3} -- these are the numbers in A such that each is a factor of 3 -- yes
    A6={1,2,3,6} -- these are the numbers in A such that each is a factor of 6 -- yes
    A8={1,2,4,8} -- these are the numbers in A such that each is a factor of 8 -- yes

    Good job!

    I find it helpful to think of the condition in "set builder notation" as a test that an entity has to pass in order to be allowed into the set -- a membership exam, if you like. So we give each element that test (and make sure that no one else would pass it), and we see that your answer is right.

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