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Intro to abstract math—basic notation

  1. Jan 13, 2016 #1
    1. The problem statement, all variables and given/known data
    Simplify the following statement as much as you can:

    (b).
    ##(3<4) \wedge (3<6)##

    2. Relevant equations
    ##\wedge= and##

    3. The attempt at a solution
    I figured that I could just write this as ##3<4<6##,
    but then I considered what if I didn't know that ##4<6##
    If it was just ##(3<x)\wedge (3<y)##, then I would have to consider that I don't know either x or y.
    Is it okay to say that ##3<4<6## though I just assume that ##4<6##?
    Or is statement already simplified enough.
    Is ##3<4, 6## a way to get around this?
     
  2. jcsd
  3. Jan 13, 2016 #2

    Mark44

    Staff: Mentor

    If 3 < 4, then 3 is automatically smaller than 6, so that latter statement is redundant.
    You know how to count to 10, right? Then you know that 4 < 6.
    No, 3 < 4, 6 is not any sort of standard notation.
     
  4. Jan 13, 2016 #3

    HallsofIvy

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    I would not say "3< 4< 6" because "3 is less than 4 and 3 is less than 6" does NOT, as you say, say that "4< 6". I think the most "simplified" form is just what I said before: "3 is less than 4 and 3 is less than 6" or perhaps "3 is less that either 4 or 6". If you take it as given that 4< 6 then "3< 4 and 3< 6" is equivalent to "3< 4" since then "3< 6" follows immediately.
     
  5. Jan 14, 2016 #4

    Fredrik

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    Gold Member

    Are you allowed to replace a statement with a symbol that means "true"? The number 1 is often used for that purpose. (0 is used for "false").

    If the problem had asked you to simplify ##\{x\in\mathbb R|(x<4)\land(x<6)\}##, I would have said ##\{x\in\mathbb R|x<4\}##. (Since 4<6, the statements "x<4" and "x<4 and x<6") are equivalent for all real numbers x). But here I don't think it makes sense to use that 4<6.

    The problem is kind of weird. It might help if you tell us where you found it.
     
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