Sentence examples for the foregoing proposition from inspiring English sources

Wittgenstein stresses that he is trying to 'warn' us against this 'aspect' the idea that the foregoing proposition about fractions "introduces us to the mysteries of the mathematical world," which exists somewhere as a completed totality, awaiting our prodding and our discoveries.

For quasi-uniform meshes with N elements and 2D BEM, this corresponds to O (N − 3 / 2 ) and hence s = 3 / 2. With the foregoing proposition and according to Theorem 4.5, the adaptive algorithm attains any possible convergence order 0 < s ≤ 3 / 2 and the generically quasi-optimal rate is thus achieved.

Then the b.v.p. (8) has a solution in Q. Combining the foregoing continuation principle with the Scorza-Dragoni-type technique (cf. Proposition 2.2), we are ready to state the main result of the paper concerning the solvability and localization of a solution of the multivalued Dirichlet problem (2).

Remark 4 In view of Proposition 1 and its analogy for q.p. sequences mentioned in the foregoing section, a discrete (i.e., restricted to ℤ) analogy of Theorem 2 holds for sequences.

However, the final circumstances could vary from the foregoing".

The foregoing came seconds before Lucas got his comeuppance.

Indeed how can any of the foregoing be objectionable?

Nature of attempts at the foregoing: brash, loud, snarling.

"All of the foregoing are subject to interpretation," he said.

Without limiting the foregoing, Client shall not: 2.4.1.

The foregoing thus must suffice concerning this matter.