Adverb:

ਮਾਮੂਲੀ,

vacuously's Usage Examples:

Finite languages vacuously satisfy the pumping lemma by having p {\displaystyle p} equal to the maximum.

Note that the theorem still holds (perhaps vacuously) for X an arbitrary Hausdorff space and Y a Hausdorff space with countable.

Elementary classes are (vacuously) pseudoelementary but the converse is not always true; nevertheless pseudoelementary.

, "it is what it is", making them appear vacuously true.

Song" railed against the duo"s perceived vacuousness in house music by (vacuously) repeating the title with no other lyrics.

material conditional analysis treats conditionals with false antecedents as vacuously true.

He endorses Massimo Mila's view that the opera demonstrates that way of making a hedonistic and vacuously melodious opera which was the norm in contemporary Italian theatres.

In pure mathematics, vacuously true statements are not generally of interest by themselves.

For example, ≥ is an antisymmetric relation; so is >, but vacuously.

For n ∈ { 1 , 2 } {\displaystyle n\in \{1,2\}} , it is vacuously true that every n × n {\displaystyle n\times n} matrix is both upper Hessenberg.

Finite languages vacuously satisfy the pumping lemma by having p equal to the maximum string length in L plus one.

b {\displaystyle aRb} and b R c {\displaystyle bRc} , and hence the transitivity condition is vacuously true.

For example, it is vacuously true that the empty set is a hereditary set, and thus the set { ∅ } {\displaystyle.