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In predicate logic, universal quantification is an attempt to formalize the
notion that something (a logical predicate) is true for everything, or
every relevant thing.The resulting statement is a universally quantified
statement, and we have universally quantified over the predicate.In
symbolic logic, the universal quantifier (typically forall ) is the symbol
used to denote universal quantification, and is often informally read as
"given any" or "for all".
Quantification in general is covered in the article on quantification,
while this article discusses universal quantification specifically.
Compare this with existential quantification, which says that something is
true for at least one thing.
Basics Suppose you wish to say
2·0 = 0 + 0, and 2·1 = 1 + 1, and 2·2 = 2 + 2, etc. This would seem to
be a logical conjunction because of
