Definition:Bounded Class/Bounded Subset of Class

Definition

Let $B$ be a class.

Let $B$ be a subclass of a class $A$.

Then $B$ is a bounded subset of $A$ if and only if:

there exists a set $x \in A$ such that $B$ is bounded by $x$

That is, if and only if every element of $B$ is a subset of $x$.

Also see

• Definition:Set Bounded by Set

Sources

• 2010: Raymond M. Smullyan and Melvin Fitting: Set Theory and the Continuum Problem (revised ed.) ... (previous) ... (next): Chapter $3$: The Natural Numbers: $\S 4$ A double induction principle and its applications: Definition $4.11$