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Contents Dark Mode Prev Up Next \(\DeclareMathOperator{\sgn}{sgn}
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Section 1.3 Predicates and quantifiers
A predicate is a function
\(f\colon X\to \mathcal{S}\text{,}\) where
\(X\) is a set and
\(\mathcal{S}\) is the set of statements.
We use the symbols \(\forall,\exists\) to denote “for all”, “there exists”, respectively. It is okay to use these shorthand symbols for informal “chalkboard” discussion and for scratchwork. In narrative writing, always use words instead. For example, in an informal discussion, one might write
\begin{equation*}
\forall x \;\; f(x)
\end{equation*}
but in formal writing, one might write
for all
\(x\) in the domain
\(X\text{,}\) the statement
\(f(x)\) holds.
