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Building a set notation

  1. May 8, 2013 #1

    reenmachine

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

    The book I'm reading ask me to build a set notation for the following set: ##\{-3/2 , -3/4 , 0 , 3/4 , 3/2 , 9/4 , 3 , 15/4 \}##.

    3. The attempt at a solution

    I attempted to build a set notation and came with the result:

    ##\{ x \in R : \exists y\in Z \ \ y(3/4)= x\}##

    My idea is that the sequence is always +3/4 or -3/4 , therefore any number in Z multiplied by 3/4 will be an element of the set we're trying to notate.

    Thank you for your help!
     
  2. jcsd
  3. May 8, 2013 #2

    Dick

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    That's true enough, but the set your notation describes has an infinite number of elements. The original set you wrote down has only 8 elements. Your notation should be a little more specific. Or does the set you are trying to construct also have an infinite number of elements and you only showed 8 of them without a '...'?
     
  4. May 8, 2013 #3

    Fredrik

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    There's also a way to simplify the notation. Fix the issue that Dick mentioned first, and then try to think of a way to simplify the notation.
     
  5. May 8, 2013 #4

    Dick

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    I agree. But I think the set reenmachine wants to describe probably has more than 8 elements. I was just trying to clear that up. It's not all that useful to describe small finite sets using set builder notation. Otherwise why not write {x:x∈{−3/2,−3/4,0,3/4,3/2,9/4,3,15/4}}?
     
  6. May 8, 2013 #5

    reenmachine

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    My apologies for the other thread , thought this one didn't work my computer crashed or something.

    I made a mistake , the set I was supposed to find a notation for was the set ##\{... , -3/2 , -3/4 , 0 , 3/4 , 3/2 , 9/4 , 3 , 15/4 , ...\}##.

    To simplify it , I could try: ##\{ n \in Z : n(3/4)\}## ?
     
  7. May 8, 2013 #6

    Mark44

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    It would be {3n/4 : n ##\in## Z}
     
  8. May 8, 2013 #7

    reenmachine

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    Is there really a difference? If so , is it the left-right factor or is it ##3n/4## versus the ##n(3/4)##?
     
  9. May 8, 2013 #8

    Dick

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    {n∈Z:n(3/4)} doesn't mean anything. What follows the ':' is supposed to be a true/false statement.
     
  10. May 8, 2013 #9

    reenmachine

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    Ok , in that case , is ##\{ n(3/4) : n \in Z\}## the same as ##\{ 3n/4 : n \in Z\}##?
     
  11. May 8, 2013 #10

    Dick

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    Sure it is. 3n/4=(3/4)n. Isn't it?
     
  12. May 8, 2013 #11

    Mark44

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    Yes, but written in a slightly different way. I reversed the order of things in what I wrote for the reason that Dick said.
     
  13. May 8, 2013 #12

    reenmachine

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    Thanks guys!

    So basically , ##\{3n/4 : n \in Z\}## is the shortest way to describe the set with a set notation?
     
  14. May 8, 2013 #13

    Dick

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    I would say, yes.
     
  15. May 8, 2013 #14

    reenmachine

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    Thanks guys!
     
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