Definitions
from Wiktionary, Creative Commons Attribution/ShareAlike License
 adj. Of a set, containing at least one element; not the empty set.
Etymologies
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Examples

If we can equate nothing with the empty set and something with a nonempty set, (not a trivial assumption, given that mathematics extends beyond set theory), then it is significant to note that whilst every set contains the empty set as a subset, the converse certainly isn't true.

Clearly the intersections of sex with both toothpaste and orange juice should be nonempty.

The ones who get hosed by the present system are those with no bargaining power and nonempty pockets.
The Volokh Conspiracy » Health Insurance and the Public Plan: Where’s The Beef?

However, this resemblance is merely apparent, because empty nouns are genuine names and can always be decomposed into nonempty genuine names (e.g., "round square").

An inclusive or exclusive disjunction of two propositions s1 and s2 is interpreted by Bolzano as a proposition which attributes to the idea [a true proposition belonging to the collection consisting of s1 and s2] the property of being nonempty or singular, respectively (WL II, 204 f., 228 f.).

A propositional form F is universally valid iff at least one member of F is true, and every member of F with a nonempty subject idea is true; F is universally contravalid iff every member of F is false.

If all ivariants of a proposition s with an nonempty subject idea are true, Bolzano will say that s is universally valid with respect to i.

If all variants of s with respect to i with nonempty subject ideas are true,

In a sentence of the form ˜There is at least one A™ we attribute, according to Bolzano, not a property to A itself but to [A], i.e., the idea of A, namely the property of being nonempty.

A propositional form F is logically valid iff F is a logical propositional form that is universally valid, i.e., at least one of its members is true, and all of its members with nonempty subject ideas are true.
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