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Math Help - Correct syntax

  1. #1
    Newbie
    Joined
    Jul 2011
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    6

    Correct syntax

    Hello

    Could you tell me which one is correct? If none of them are, could you write the correct format?


    \existsj j \in myset


    \existsj, j \in myset


    \exists j \wedge" alt="\wedge" /> j \in myset
    which I could not get to display properly, but it is

    \exists j logical and j \in myset

    Thank you all!
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  2. #2
    MHF Contributor
    Joined
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    Re: Correct syntax

    ∃j ∧ j ∈ myset is wrong because ∧ has to join two well-formed formulas, and ∃j is not a complete formula. Whether to put a comma after ∃j is purely a question of definitions and conventions.

    In the most unfolded form, the statement "there exists a j in myset such that P(j)" can be written as ∃j (j ∈ myset ∧ P(j)). Often it is abbreviated to ∃j ∈ myset, P(j). However, this refers to unsorted logic, where variables don't have an intrinsic range, or sort, and j ∈ myset is a proposition. There are other logic languages where one must specify a variable's sort when the variable is introduced. Then ∃j ∈ myset or ∃j : myset is an indivisible expression that does not stand for ∃j (j ∈ myset ∧ ...).
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