Definition: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.

Also see

• Implicit Set Definition
• Set Definition by Predicate

Sources

• Steven A. Gaal: Point Set Topology (1964)... (previous)... (next): Introduction to Set Theory: $1$. Elementary Operations on Sets
• J.A. Green: Sets and Groups (1965)... (previous)... (next): $\S 1.1$: Example $4$
• Seth Warner: Modern Algebra (1965)... (previous)... (next): $\S 1$
• K.G. Binmore: Mathematical Analysis: A Straightforward Approach (1977)... (previous)... (next): $\S 1.1$