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.

## DetailsDetails

• 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 .
• 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.

## ExamplesExamplesopen allclose all

### Basic Examples (1)Basic Examples (1)

This states that there exists a positive solution to the equation :

 Out[1]=

Use Resolve to get a condition on real parameters for which the statement is true:

 Out[2]=

Reduce gives the condition in a solved form:

 Out[3]=