A partition is possible ( of a set with 0 elements into 0 parts ), but since the partition has 0 parts, vacuously every set in our partition has a given number of elements, be it 0, 2, 5, or 1000.
32.
Under the first representation it is vacuously true that if you commit a forbidden act, then you ought to commit any other act, regardless of whether that second act was obligatory, permitted or forbidden ( Von Wright 1956, cited in Aqvist 1994 ).
33.
The bottom element is the supremum of the empty set, i . e . the element containing no information at all; its existence is implied by bounded completeness, since, vacuously, the empty set has an upper bound in any non-empty poset.
34.
Implicitly she is critical of much of the motivational industry that has flourished in the face of employment insecurity and instability; on one character assessment she is described, rather superficially and vacuously, as'Original and Effective'and on another as'the commandant '.
35.
The trivial case of generating " a ", in case it is difficult to see, simply involves vacuously applying r _ 1, thus jumping straight to r _ 2 which also vacuously applies, then jumping to r _ 3 which produces " a ".
36.
The trivial case of generating " a ", in case it is difficult to see, simply involves vacuously applying r _ 1, thus jumping straight to r _ 2 which also vacuously applies, then jumping to r _ 3 which produces " a ".
37.
When Carlo smiles vacuously at Francesca ( the screen debut by Martina Stella, who's reminiscent of a young Reese Witherspoon, if that's not redundant ), you get the urge to slap him, though it's a good bet that Giulia will take care of that.
38.
It should also be noted that the definition of ?% makes vacuously true certain sentences, since when it speaks of " every world that is accessible to " w " " it takes for granted the usual mathematical interpretation of the word " every " ( see vacuous truth ).
39.
Intuitively, this simply spells out that a rule can apply to a string if the rule's left-hand-side appears in that string, or if the rule is in the set of " vacuously applicable " rules which can " apply " to a string without changing anything.
40.
Then the empty subset of " P " is a chain, as it satisfies the definition vacuously; so the hypothesis implies that this subset must have an upper bound in " P ", and this upper bound shows that " P " is in fact non-empty.
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