It is comprehensive, factually accurate, well-written, uncontroversial, some of the best work on Wikipedia, contains a brief but sufficient lead section, includes images where appropriate ( vacuously true ), has subheads, has a substantial but not overwhelming table of contents, and complies with the standards set by any relevant wikiprojects.
42.
I prepare back-of-the-book indexes for nonfiction books, but with the exception of other people who work in publishing, I usually get one of three responses when I say that I am an indexer or a book indexer _ a blank look, a quick change of subject or a vacuously polite " That's nice ."
43.
"For any integer x, if x > 5 then x > 3 . " This statement is true non-vacuously ( since some integers are greater than 5 ), but some of its implications are only vacuously true : for example, when x is the integer 2, the statement implies the vacuous truth that " if 2 > 5 then 2 > 3 ".
44.
"For any integer x, if x > 5 then x > 3 . " This statement is true non-vacuously ( since some integers are greater than 5 ), but some of its implications are only vacuously true : for example, when x is the integer 2, the statement implies the vacuous truth that " if 2 > 5 then 2 > 3 ".
45.
Baldini notes that there is slight musical value in the opera and that Verdi's contribution is at best superficial since it merely reflects ( and here he quotes from Massimo Mila's 1958 work on Verdi ) " that way of making a hedonistic and vacuously melodious opera which was the norm in contemporary Italian theatres . " However, Baldini mentions one or two numbers which, in his opinion, have some merit.
46.
Intuitively, when applying a rule " p " in a programmed grammar, the rule can either succeed at rewriting a symbol in the string, in which case the subsequent rule must be in " p " s success field, or the rule can fail to rewrite a symbol ( thus applying vacuously ), in which case the subsequent rule must be in " p " s failure field.
47.
But Ellis's satirical message is, essentially, a one-liner, and hardly an original one at that-- celebrity culture is vapid, yes, and ?-- and isn't remotely worth the endless pages in which his vacuous and inconsequential characters talk vacuously and inconsequentially about vacuous and inconsequential things : " I'm seeing Emily Lloyd maintaining remarkable poise while eating a giant grilled shrimp ."
48.
On Lewis's account, A > C is ( a ) vacuously true if and only if there are no worlds where A is true ( for example, if A is logically or metaphysically impossible ); ( b ) non-vacuously true if and only if, among the worlds where A is true, some worlds where C is true are closer to the actual world than any world where C is not true; or ( c ) false otherwise.
49.
On Lewis's account, A > C is ( a ) vacuously true if and only if there are no worlds where A is true ( for example, if A is logically or metaphysically impossible ); ( b ) non-vacuously true if and only if, among the worlds where A is true, some worlds where C is true are closer to the actual world than any world where C is not true; or ( c ) false otherwise.
50.
So, it's more like defining continuity by " it's smooth and doesn't have an holes " than by " The limit of f ( x ) as x approaches c must exist and be equal to f ( c ) . ( If the point c in the domain of f is not an accumulation point of the domain, then this condition is vacuously true, since x cannot approach c . ) " ( from the relevant article ).
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