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Built-in Functions / Algebraic Computation / Formula Manipulation /

ForAll

Usage

• 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 .


Notes

• ForAll[x, expr] can be entered as . The character can be entered as AliasIndicatorfaAliasIndicator 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.
Further Examples


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