Definition:Ordinary Set

Definition

Let $S$ be a set.

Then $S$ is an ordinary set if and only if:

$S \notin S$

That is, if and only if $S$ is not an element of itself.

Also known as

Some sources refer to such a set as a normal set.

Also see

• Definition:Extraordinary Set

• Results about ordinary sets can be found here.

Sources

• 1963: George F. Simmons: Introduction to Topology and Modern Analysis ... (previous) ... (next): $\S 1$: Sets and Set Inclusion
• 2010: Raymond M. Smullyan and Melvin Fitting: Set Theory and the Continuum Problem (revised ed.) ... (previous) ... (next): Chapter $1$: General Background: $\S 8$ Russell's paradox