Sentence examples for for a finite subset of from inspiring English sources

In this paper, we define the concept of a spherical T-design for a finite subset of a sphere.

Thus, the P(G P(D)) values for a finite subset of compound-target vectors x i,..,x n follow a multidimensional normal distribution with mean μ and covariance matrix C X : GP ( D ) ∼ N 0, C X + σ d 2 δ x j, x k j,k ∈ 1, …, n (2).

Then each binary number may be viewed as the characteristic function of a finite subset of natural numbers.

Then for each there exists a finite subset of and a function such that for all.

Suppose that there exists a finite subset of and for all with such that for each.

Hence for each natural number we may choose a finite subset of and a map such that.

Consider a sequence of index sets { M k } k = 0 ∞, where for all k ≥ 0, M k is a finite subset of Σ ∗.

Let \((G, \cdot)\) be a group and \(S\) a finite subset of \(G\).

We change a finite subset of these numbers.

Then (mathcal{F}) is a finite subset of (mathcal{C}).

Hence, employing a finite subset of the infinite chain of reasons could, on some occasions, suffice for reaching the requisite threshold of this feature of justification required for distinctively adult human knowledge.