Definition:Set/Explicit Set Definition

Definition
A (finite) set can be defined by explicitly specifying all of its elements between the famous curly brackets, known as set braces: $\set {}$.

For example, the following define sets:


 * $S = \set {\textrm {Tom, Dick, Harry} }$


 * $T = \set {1, 2, 3, 4}$


 * $V = \set {\textrm {red, orange, yellow, green, blue, indigo, violet} }$

When a set is defined like this, note that all and only the elements in it are listed.

This is called explicit (set) definition.

It is possible for a set to contain other sets. For example:


 * $S = \set {a, \set a }$

Note here that $a$ and $\set a$ are not the same thing.

While it is true that:
 * $a \in \set a$

it is not true that:
 * $a = \set a$

Also known as
Some sources refer to this as a roster for the set.

Others call it an enumeration or a listing.

Also see

 * Definition:Implicit Set Definition
 * Definition:Set Definition by Predicate