If a proposition 
is true for all 
,
this is written 
.
is one of the two so-called quantifiers, and translates the universal
quantifier 
.
The Wolfram Language expression ForAll[x, expr] can be used to represent the statement that expr is true for all values of x.
See also
Almost All, Exists, For Some, Implies, Quantifier, Universal Quantifier, Universal Sentence
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Cite this as:
Weisstein, Eric W. "For All." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/ForAll.html