Sentence examples for be an arbitrary set from inspiring English sources

Let G be a group and Ω be an arbitrary set.

Let be an arbitrary set and any linear metric space.

Let G ⊂ B Ω be an arbitrary set.

Let I be an arbitrary set, which may be empty, finite, or infinite.

Let ( X, d ) be a metric space and Y be an arbitrary set.

Let R be an arbitrary set of outcomes at the physical layer.

If n is a natural number and A is an arbitrary set, the expression An is often used to denote the set of ordered n-tuples of elements of A. This is equivalent to letting An denote the set of functions from the set {0, 1, 2, …, n−1} to the set A; the n-tuple (a0, a1, a2, …, an−1) represents the function that sends i to ai.

Relatively recently it was proved that if Γ is an arbitrary set, then any equivalent norm on c0 can be approximated uniformly on bounded sets by polyhedral norms and C∞ smooth norms, with arbitrary precision.

Since is an arbitrary set, it follows that (4.20).

where is the set of Lebesgue measure zero where does not exist, and is an arbitrary set with measure zero.

Let D be an open subset of a topological space X and (f:Dto Y) be an operator where Y is an arbitrary set.