Category:Definitions/Inductive Classes

This category contains definitions related to Inductive Classes.
Related results can be found in Category: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 4 subcategories, out of 4 total.

The following 8 pages are in this category, out of 8 total.