ForAll

ForAll[x, expr] represents the statement that expr is True for all values of x.

ForAll[x, cond, expr] states that expr is True for all x satisfying the condition cond.

ForAll[, , ... , expr] states that expr is True for all values of all the .

ForAll[x, expr] can be entered as . The character can be entered as fa or \[ForAll]. The variable x is given as a subscript.

ForAll[x, cond, expr] can be entered as .

In StandardForm, ForAll[x, expr] is output as .

ForAll[x, cond, expr] is output as .

ForAll 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 x Integers.

ForAll[x, cond, expr] is equivalent to ForAll[x, Implies[cond, expr]].

ForAll[, , ... , ... ] is equivalent to .

The value of x in ForAll[x, expr] is taken to be localized, as in Block.

See Section 3.4.11.

See also: Exists, Resolve, Reduce, Element, Blank, SolveAlways.

New in Version 5.0.

Further Examples