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: $\left\{{}\right\}$.

For example, the following define sets:


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


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


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

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:


 * $S = \left\{{a, \left\{{a}\right\}}\right\}$

Note here that $a$ and $\left\{{a}\right\}$ are not the same thing.

While it is true that:
 * $a \in \left\{{a}\right\}$

it is not true that:
 * $a = \left\{{a}\right\}$

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