nLab example

Idea

In mathematics, an example for a proposition with a universal quantifier $\big({\forall}_{x \in X} \; P(x)\big)$ or an existential quantifier $\big(\underset{x \in X}{\exists}\; P(x) \big)$ is a term $x$ of type $X$ for which $P(x)$ is true (inhabited).

Examples

• examples of Kan extensions

• Every counterexample is an example of the negation of a proposition.

Related concepts

mathematical statements

• theory

• judgement, assertion

• hypothesis, consequence

• axiom

• assignment

• definition (inductive, coinductive)

• lemma

• proposition/type (propositions as types)

• theorem

• proof/program (proofs as programs)

• example, counterexample

• conjecture, folklore

• exercise

• analogy

• tautology

• paradox

See also

• archetypal example