Vacuous truth

Conditional statement which is true because the antecedent cannot be satisfied

Examples common to everyday speech include conditional phrases used as idioms of improbability like "when hell freezes over..." and "when pigs can fly...", indicating that not before the given (impossible) condition is met will the speaker accept some respective (typically false or absurd) proposition.

Many programming environments have a mechanism for querying if every item in a collection of items satisfies some predicate. It is common for such a query to always evaluate as true for an empty collection. For example: