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inductive set (Definition)

An inductive set is a set $ X$ with the property that, for every $ x \in X$, the successor $ x'$ of $ x$ is also an element of $ X$.

One major example of an inductive set is the set of natural numbers $ \mathbb{N}$.



"inductive set" is owned by djao.
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See Also: natural number

Other names:  successor set
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Cross-references: natural numbers, successor, property
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This is version 7 of inductive set, born on 2001-10-19, modified 2003-11-05.
Object id is 386, canonical name is InductiveSet.
Accessed 8197 times total.

Classification:
AMS MSC: 03E20 (Mathematical logic and foundations :: Set theory :: Other classical set theory )
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