Category:Inductive Classes
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This category contains results about Inductive Classes.
Definitions specific to this category can be found in Definitions/Inductive Classes.
Let $A$ be a class.
Then $A$ is inductive if and only if:
| \((1)\) | $:$ | $A$ contains the empty set: | \(\ds \quad \O \in A \) | ||||||
| \((2)\) | $:$ | $A$ is closed under the successor mapping: | \(\ds \forall x:\) | \(\ds \paren {x \in A \implies x^+ \in A} \) | where $x^+$ is the successor of $x$ | ||||
| That is, where $x^+ = x \cup \set x$ |
Subcategories
This category has the following 6 subcategories, out of 6 total.
G
I
M
S
T
Pages in category "Inductive Classes"
The following 2 pages are in this category, out of 2 total.