Sentence examples for be an arbitrary subset from inspiring English sources

Let be an arbitrary subset of.

Now, let be an arbitrary subset of such that.

Use Corollary 3.7 and observe that S may be an arbitrary subset of ({1,2,3}).

Definition 3.2 Let Y be an arbitrary subset of a b-metric space ( X, d ) and S, T : Y → X.

Let (ngeq2) be an integer and let T be an arbitrary subset of ({1,2,ldots, n-1}).

Let λ be an FK-space, U be a triangle, V be its inverse and μ be an arbitrary subset of ω.

(H4) The function such that where is an arbitrary subset of, and is bounded by for all.

In the sequel, we utilize a notation ( a, b ) M = ( a, b ) ∩ M, where M is an arbitrary subset of reals (analogously for closed intervals).

Suppose that ((X,M,ast)) is the same as in Example 1.3, (Ain X) is an arbitrary subset of X and (x_{0}notin A), then (M x_{0},A,t leq frac{1}{2}).

Thus L allows arbitrarily long conjunctions and disjunctions, in the sense that if Φ is an arbitrary subset of Form, then both ∧Φ and ∨Φ are members of Form.

Kripke defines a model over a non-empty domain D of individuals as an ordered pair (G, K), such that G∈K, K is an arbitrary subset of assignments of values to the formulas of S5*=, and all H∈K agree on the assignments to individual variables.