Wolfram Language & System 10.0 (2014)|Legacy Documentation

This is documentation for an earlier version of the Wolfram Language.
BUILT-IN WOLFRAM LANGUAGE 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 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.

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]=