BUILT-IN MATHEMATICA SYMBOL

Exists

Exists[x, expr]
represents the statement that there exists a value of x for which expr is True.

Exists[x, cond, expr]
states that there exists an x satisfying the condition cond for which expr is True.

Exists[{x₁, x₂, ...}, expr]
states that there exist values for all the for which expr is True.

Details Details

Exists[x, expr] can be entered as . The character can be entered as EscexEsc or \[Exists]. The variable is given as a subscript.
Exists[x, cond, expr] can be entered as .
In StandardForm, Exists[x, expr] is output as .
Exists[x, cond, expr] is output as .
Exists can be used in such functions as Reduce, Resolve, and FullSimplify.
The condition cond is often used to specify the domain of a variable, as in xIntegers.
Exists[x, cond, expr] is equivalent to Exists[x, cond&&expr].
Exists[{x₁, x₂, ...}, ...] is equivalent to .
The value of in Exists[x, expr] is taken to be localized, as in Block.