vacuously

An adverb used in logic, mathematics, and formal reasoning meaning "in a vacuous manner" or "without content." It describes a statement that is true by default because the condition it depends on cannot be satisfied (e.g., "all unicorns are pink" is vacuously true).

• 🇪🇸Adverbio usado en lógica, matemáticas y razonamiento formal, que significa 'sin contenido' o 'vacuamente'. Describe una afirmación que es verdadera por defecto porque la condición de la que depende no puede cumplirse (por ejemplo, 'todos los unicornios son rosados' es verdadera en sentido vacío).

1. In a mindless or empty way C2 formal

   In a manner that shows a lack of thought, intelligence, or purpose.

   • He stared vacuously at the television screen.
   • She smiled vacuously, not understanding the joke.
   • The audience listened vacuously to the long lecture.

   🇪🇸de manera vacía

   Sinónimos: blanklyinanelymindlesslystupidlythoughtlesslyunintelligently

   Antónimos: intelligentlymeaningfullypurposefullythoughtfully

2. In logic: true by default C2 formal

   In logic, a statement is said to be vacuously true if its antecedent is false, making the implication true regardless of the consequent.

   • The statement 'All unicorns are pink' is vacuously true because there are no unicorns.
   • In mathematics, a property holds vacuously for an empty set.
   • The theorem is vacuously satisfied when the condition cannot be met.

   🇪🇸Verdadero por vacuidad

   Sinónimos: trivially

• more vacuously comparative form
• most vacuously superlative form