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What is the notation for the statement for some integer n ?

  1. Oct 17, 2006 #1
    What is the notation for the statement "for some integer n"?

    What is the notation for the statement "for some integer n"?
    Is it [tex] \forall n | n \in Z [/tex]
    Or is it [tex] \{n | n \in Z \} [/tex]

    Or is it something else?

    [tex]|[/tex] does mean "such that", doesn't it?
     
    Last edited: Oct 17, 2006
  2. jcsd
  3. Oct 17, 2006 #2

    Office_Shredder

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    The first notation you show means for all integers n. The second is the set of all integers. What you're looking for, I think, is notation that indicates there exists at least one n that the statement is true for. I don't know how to make the symbol in latex, but it looks like a backwards capital E. Pretending my E is actually backwards for the purposes of this:

    Example:

    E n s.t.[tex]\sqrt{9} = n[/tex]

    could be read as there exists n such that the square root of 9 equals n. Alternatively, you could say the square root of 9 equals n for some n
     
    Last edited: Oct 17, 2006
  4. Oct 17, 2006 #3
    What is the symbol for "such that"?
     
  5. Oct 17, 2006 #4
    Tell me if I am interpreting my first two notations correctly.
    I would read [tex] \forall n | n \in Z [/tex] as "for all n such that n is an element of the set of integers".

    And I would read [tex] \{n | n \in Z \} [/tex] as "the set of n such that n is an element of the set of integers".
     
  6. Oct 17, 2006 #5

    Office_Shredder

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    First, I found how to do the symbol:

    [tex]\exists n \in Q s.t. n \in Z[/tex]

    reads there exists n a rational such that n is an integer (a trivial statement, I admit :) ).

    generally, the vertical bar is only used in your second example, for your first example it would be better to put s.t. (for such that).
     
  7. Oct 17, 2006 #6
    What do you mean "there exists n a rational"?
     
  8. Oct 17, 2006 #7
    Off the topic, but do you know what the RMS voltage is of a triangle wave?
     
    Last edited: Oct 17, 2006
  9. Oct 17, 2006 #8

    HallsofIvy

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    Better grammar: there exist a rationa number n such that n is an integer.
     
  10. Oct 17, 2006 #9
    That makes more sense. Thanks.
     
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