# Correct syntax

• Sep 27th 2011, 04:40 PM
Tina
Correct syntax
Hello

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

$\exists$j j $\in$ myset

$\exists$j, 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!
• Sep 28th 2011, 03:23 AM
emakarov
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 ∧ ...).