Category:Definitions/Inductive Sets
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This category contains definitions related to Inductive Sets.
Related results can be found in Category:Inductive Sets.
Let $S$ be a set of sets.
Then $S$ is inductive if and only if:
| \((1)\) | $:$ | $S$ contains the empty set: | \(\ds \quad \O \in S \) | ||||||
| \((2)\) | $:$ | $S$ is closed under the successor mapping: | \(\ds \forall x:\) | \(\ds \paren {x \in S \implies x^+ \in S} \) | where $x^+$ is the successor of $x$ | ||||
| That is, where $x^+ = x \cup \set x$ |
Pages in category "Definitions/Inductive Sets"
The following 4 pages are in this category, out of 4 total.