Sentence examples for be any nonempty set from inspiring English sources

Let be any nonempty set.

[14] Let A be any nonempty set.

Let Ξ be any nonempty set.

Let X be any nonempty set.

Definition 1 Let X be any nonempty set.

Let G, G1, G2, and K be groups and A be any nonempty set.

Throughout this paper, Δ = { ( x, x ) : x ∈ X } denotes the diagonal of X × X, where X is any nonempty set.

This is formally defined as follows: where \(I\) is any nonempty set of players.

If is any nonempty set, we say that the operator satisfies if for each, the mapping satisfies.

If S is any nonempty set, then (B(S)) denotes the set of all bounded functions (f:Srightarrowmathbb{R}), which is known to be a Banach algebra with the pointwise multiplication and the norm (Vertcdot Vert_{infty}) (see, for instance, [11]).

But strong global supervenience fails to entail strong individual supervenience, at least when A and B are any nonempty sets of properties.