Sentence examples for the preceding definition from inspiring English sources

Let us comment on the preceding definition.

If in the preceding definition the order is reversed then we will use the term 'deflationary' instead of inflationary.

It is clear from the preceding definition that is a solution of problem (2.3 - 2.4 2.3 - 2.4

Theorem 2.5 gives sufficient conditions for the existence of a family of functions (v k ) as in the preceding definition, but these conditions are not necessary.

Note that from the preceding definition, concretely from statements (p1) and (p2), it follows that p ( x, y ) = 0 implies that x = y.

If the gauge (delta_{varepsilon}) in the preceding Definition 8(i) can be chosen as a positive constant, then the function h is called Riemann-Stieltjes integrable with respect to T (and likewise for Definition 8 ii)).

It is a basic problem, and by no means a simple one, to show that the intuitive notion of choosing a number at random from [0, 1], as described above, is consistent with the preceding definitions.

It is clear from the preceding definitions that (partial _R A=partial ^+_R Asqcup partial ^-_R A).

In consequence the preceding definitions of logical truth, logical falsity and logical analyticity are not applicable to purely logical propositions, since they do not contain any extra-logical idea.

Analogously, we introduce ϕ ˜ n, i ( x ), ϕ ˜ ( x ) and H ˜ n, i ; k, j ( x ), H ˜ ( x ) by the replacement of S n, i ( x ), P n, i ; k, j ( x ) in the preceding definitions with S ˜ n, i ( x ), P ˜ n, i ; k, j ( x ), respectively.

(The notation g p was defined in the paragraph preceding Definition 6).