Teilnatürliche

Teilnatürliche is not a widely established term in mathematics or in German mathematical literature. As a compound, it literally means “part-natural” and could be used informally to refer to a subset of the natural numbers selected according to a rule. Because it is not standardized, its precise meaning depends on the source and context.

In practice, one might encounter “Teilnatürliche Zahlen” to denote the numbers in N that satisfy a given predicate P(n). For example, the even natural numbers or natural numbers within a certain interval could be described in this way if the author defines P(n) accordingly. The phrase points to a selected portion of the natural numbers rather than to all of N.

Because the term is nonstandard, readers should consult the exact definition in the text where it appears. In rigorous or formal writing, it is preferable to use precise terms such as Teilmenge der natürlichen Zahlen (a subset of the natural numbers) or N0 = { n ∈ N | P(n) } to avoid ambiguity.

Etymologically, the word combines Teil (part) and natürlich (natural), reflecting a common German practice of naming a subset by indicating it is part of the naturals. If encountered, the term should be interpreted through its given definition, rather than assumed to have a fixed, universal meaning.

See also: natural numbers, subset, predicate, constructive mathematics.