This is documentation for Mathematica 6, which was
based on an earlier version of the Wolfram Language.

# ForAll ()

 ForAll[x, expr]represents the statement that expr is True for all values of . ForAll[x, cond, expr]states that expr is True for all x satisfying the condition cond. ForAll[{x1, x2, ...}, 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 Esc fa Esc or \[ForAll]. The variable is given as a subscript.
• ForAll[x, cond, expr] can be entered as .
• ForAll[x, cond, expr] is output as x, condexpr.
• The condition cond is often used to specify the domain of a variable, as in .
• ForAll[{x1, x2, ...}, ...] is equivalent to .
• The value of in ForAll[x, expr] is taken to be localized, as in Block.
This states that for all , is positive:
 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]=
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