In virtue of property (19) proved above, the limit (lim_{M_{k}toinfty} vert G^{ k)}_{r,n,f,M_{k}}(0) vert ) does not depend on the choice of the sequence ({M_{k}}_{k=1}^{infty}).
end{aligned}Letting (krightarrow infty ) in above inequality and using (3.8), (3.9) and continuities of (varphi ) and (zeta,) we get begin{aligned} varphi (epsilon )le varphi (epsilon )-zeta (epsilon ) end{aligned}which is a contradiction by virtue of property of (zeta.) Therefore, the sequence ({g(x_m)}) is Cauchy.
The non-abstract set theorist will hold that a set of gold atoms can in fact have physical properties, in virtue of the properties of its members.
They have these causal properties in virtue of the properties of their parts; e.g., the imperviousness (to gas molecules) and angle of the fan blade cause gas molecules that hit it to move in certain directions.
The type is thus a very important theoretical object, whose function is to unify all the tokens as being "of the same type"; in accordance with the Platonic Relationship Principle, the type has properties based on the properties of some of its tokens, but in a complex way in addition, the tokens have some of their properties in virtue of what properties the type has.
(Even in cases of testimony, we hold that the aesthetic properties of a thing hold in virtue of nonaesthetic properties that the aesthetic expert knows).
In the present study, ZnO was selected for the composite plating by virtue of its properties like semiconductivity (band gap of 3.37 eV), piezoelectric property and biocompatibility.
We may very well use such thermodynamic properties in identifying something as water, but that does not mean that it is in virtue of such properties that something is water.
He clearly denies a crucial assumption of his critics, namely, that causes do their causing in virtue of their properties.
One may ask by virtue of which properties true and false are to be considered as logical values.
