vacuously (Meaning)

Wordnet

vacuously (r)

in a vacuous manner

The argument is vacuously true because it assumes a premise that is never met.
The statement is vacuously false since its antecedent is always false.
The theorem holds vacuously for the empty set as there are no elements to consider.
The function is vacuously continuous at a point where it is undefined.
The hypothesis is vacuously satisfied when the domain is empty.
The equation has a vacuous solution if the left-hand side is always zero.
The inequality is vacuously true if the right-hand side is always non-negative.
The set is vacuously compact since it contains no points.
The property is vacuously fulfilled if the set under consideration is empty.
The proof is vacuously correct because it assumes a proposition that has already been proven.

in a vacuous manner

empty,devoid, barren,blank, vacant, drained, stark, hollow, void, bare

full, complete, replete, full, replete, complete, furnished, supplied, provided, furnished

The argument is vacuously true because it assumes a premise that is never met.

The statement is vacuously false since its antecedent is always false.

The theorem holds vacuously for the empty set as there are no elements to consider.

The function is vacuously continuous at a point where it is undefined.