Sentence examples for conclusion of proposition from inspiring English sources

This leads to the monumental conclusion of Proposition 11: "God, or substance consisting of infinite attributes, each of which expresses eternal and infinite essence, necessarily exists".

Equation (3.4) is exactly the conclusion of Proposition 3.7.

The following example illustrates that we cannot replace K̃ by C in the conclusion of Proposition 3.5.

It can be seen from Figure 2 that the shape change of the generalized Bézier-like surfaces accords with the conclusion of Proposition 1. Figure 2 Generalized Bézier-like surfaces of degree (pmb{ 3, 3)}) with different shape parameter λ.

On the basis of the conclusion of Proposition 1 and Proposition 2 and the control mesh points kept unchanged, we have the following: (a) with the simultaneous increase (or decrease) of the shape parameters λ, (gamma_{i}) ((i = 0,1, ldots,m)), the generalized Bézier-like surfaces gradually get nearer to (or farther away from) their control mesh.

In particular, for (s=2), a similar reasoning as the one in the proof of the property (P) above shows that the conclusion of Proposition 4.4 implies lim_{nto+infty}|F_{R^{ntau}theta_{2}^{(f)} vartheta _{1},vartheta_{2},cdot)}-F_{R^{2alpha}f}|=0, as soon as (vartheta_{1}neqvartheta_{mathrm{unst}}) and (vartheta _{2}neqvartheta_{mathrm{unst},2}).

Therefore, the conclusions of Proposition 1.2 hold.

Because every subsequence of is also an approximate fixed point sequence, the conclusions of Proposition 3.1 still stand for.

Hence the conclusions of Proposition 3.3 also hold for the equation F ( x ) = 0. Remarks 3.6 [1, 6, 7] (1) The condition (3.32) can be replaced by a stronger, but easier to check 2 η 2 − δ ≤ p 0, (3.44)  .

The next proposition specifies what are the conditions for a majority winner to exist and such that the conclusions of Proposition 3.4 remain valid, even if there cannot be formed a majority by individuals between the upper part of the low income group and the lower part of the high income group.

Indeed if T is continuous at (x^ ), then the conclusion of the proposition holds true, hence it suffices for us to show that (lim_{ntoinfty}Tx_{n}=Tx^ ) for every sequence ({x_{n}}_{ngeq0} ) converging to (x^ ).