Sentence examples for be a proper subset from inspiring English sources

Let (mathcal {Q}) be a proper subset of (mathcal {S}) such that (|mathcal {Q}| = alpha n).

Next suppose R is finite and let S be a proper subset of R with |S|⩾2.

More generally, a sufficient condition for T1 being more parsimonious than T2 is for the ontological commitments of T1 to be a proper subset of those of T2.

It is illustrated by an example that under the conditions the maximal domain of existence of a solution of (1.1) may be a proper subset of.

Invoke a function that for each Γ produces a subset MΓ of the models of Γ; in general, we will expect MΓ to be a proper subset of these models.

In other cases, however, there will be some additional restrictions on C, i.e., it will be a proper subset of the set of all maximally ordered linear subsets in (TIME,≤).

Killing oneself is a proper subset of killing in general, and should not be allowed.

If every element of set B is an element of set A, but the converse is false (hence B ≠ A), then B is said to be properly included in, or is a proper subset of, A (symbolized by B ⊂ A).

Still summarizing Galileo, he writes that "an infinite set, the set of all whole numbers, is shown to be 'equal in number' to the set of all squares of whole numbers, which is a proper subset of the set of whole numbers".

The possibilist maintains that what actually exists is a proper subset of what exists.

Since is surjective and satisfies (2.18), is a proper subset of.