View example sentences and word forms for Vacuously.
Vacuously meaning
In a vacuous manner, lacking thought. | Because of being a vacuous truth.
Example sentences (4)
In this case, the statement "all cell phones in the room are turned on" would also be vacuously true, as would the conjunction of the two: "all cell phones in the room are turned on and turned off".
Note that the empty set is a subset of every set (the statement that all elements of the empty set are also members of any set A is vacuously true ).
Outside of mathematics, statements which can be characterized informally as vacuously true can be misleading.
Proof: If there is no possible move, then the lemma is vacuously true (and the first player loses the normal play game by definition).