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Largest x for which an equation is true

  1. Feb 23, 2012 #1
    1. The problem statement, all variables and given/known data
    How to use mathematical notation to express the largest x for which an equation is true?

    For example, how to express the largest x for which A(x) = B(x)? I need to be able to give the instruction to find the largest x for which A(x) = B(x) is true, but I wonder if it can be written down in a more algebraic manner, instead of relying purely on language.

    2. Relevant equations
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    3. The attempt at a solution
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  2. jcsd
  3. Feb 23, 2012 #2

    Mark44

    Staff: Mentor

    max{x [itex]\in[/itex] R : A(x) = B(x)}

    In words, this repesents the largest real number x for which A(x) = B(x). You didn't say, but I'm assuming you mean real number values.

    Typically, this would be a set with a finite number of values in it, of which you want the largest. If the solution set of the equation A(x) = B(x) has infinitely members, there won't be a largest value.
     
  4. Feb 24, 2012 #3
    Thanks a lot for your input.

    How is the type of notation which is used in this case called? What branch of mathematics does it belong to (especially the max operator)? Formal logic?
     
  5. Feb 24, 2012 #4

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    [itex]\{x\in R: A(x)= B(x)\}[itex] is "set buider notation". It specifices the set of all real numbers, x, such that A(x)= B(x). And the "max" in front is an operator that returns the largest member of the set.
     
  6. Feb 24, 2012 #5
    Thanks for your input.

    Is there any documentation of the max operator? Is it recognized in the mainstream mathematics?
     
  7. Feb 24, 2012 #6

    Mark44

    Staff: Mentor

    You are way overthinking this. When applied to a set for which it makes sense (finite set of elements that have an inherent ordering), the max of the set is the largest element.

    This is well known in mathematics.

    Putting on my moderator hat: You now have three or four threads, all asking more-or-less the same question. Do not start a new thread on this same subject.
     
  8. Feb 24, 2012 #7
    Sorry for butting in, but did you actually mean to say that?

    What if the solution set was:

    [itex]\{ x \in \mathbb{R} : 0 \leq x \leq 1 \}[/itex]

    or

    [itex]\{ n \in \mathbb{Z} : n \leq 0 \}[/itex]

    to take two very simple examples?

    These two sets both have infinitely many members, but they each have a largest value (1 and 0, respectively).

    Apologies if I have misunderstood.
     
  9. Feb 24, 2012 #8

    Mark44

    Staff: Mentor

    Thanks for correcting me - you're absolutely right. I was thinking in terms of solutions to various kinds of equations, where the solutions are discrete, and didn't consider the possibility of a solution set that was bounded interval.
     
  10. Feb 27, 2012 #9
    Strange reply, but I'm sure you know what you're talking about! :smile:
     
  11. Feb 27, 2012 #10
    The correct correction is: An infinite set of reals does not necessarily have a largest element. Of course some sets of reals do have a largest element.
     
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