# Category:Examples of Sets

This category contains examples of Set.

A **set** is intuitively defined as any aggregation of objects, called elements, which can be precisely defined in some way or other.

We can think of each set as a single entity in itself, and we can denote it (and usually do) by means of a single symbol.

That is, *anything you care to think of* can be a set. This concept is known as the comprehension principle.

However, there are problems with the comprehension principle. If we allow it to be used without any restrictions at all, paradoxes arise, the most famous example probably being Russell's Paradox.

Hence some sources define a **set** as a ** 'well-defined' collection of objects**, leaving the concept of what constitutes well-definition to later in the exposition.

## Pages in category "Examples of Sets"

The following 29 pages are in this category, out of 29 total.

### E

- Explicit Set Definition/Examples
- Explicit Set Definition/Examples/Example 1
- Explicit Set Definition/Examples/Example 10
- Explicit Set Definition/Examples/Example 11
- Explicit Set Definition/Examples/Example 2
- Explicit Set Definition/Examples/Example 3
- Explicit Set Definition/Examples/Example 4
- Explicit Set Definition/Examples/Example 5
- Explicit Set Definition/Examples/Example 6
- Explicit Set Definition/Examples/Example 7
- Explicit Set Definition/Examples/Example 8
- Explicit Set Definition/Examples/Example 9

### S

- Set Definition by Predicate/Examples/Cube Numbers
- Set Definition by Predicate/Examples/Integers Greater Than or Equal to 2
- Set Definition by Predicate/Examples/Integers Less Than or Equal to 5
- Set Definition by Predicate/Examples/Musical Mathematicians
- Set Definition by Predicate/Examples/People who Love Romeo
- Set Definition by Predicate/Examples/Set Indexed by Natural Numbers between 1 and 10
- Set Definition by Predicate/Examples/Set Indexed by Natural Numbers between 1 and 100
- Set Definition by Predicate/Examples/Sums of Two Squares
- Set Definition by Predicate/Examples/United States Senate
- Set Definition by Predicate/Examples/University Professors
- Set/Definition by Predicate/Examples
- Set/Examples
- Set/Examples/Living People
- Set/Examples/People Called Smith
- Set/Examples/Positive Integers Less than 10
- Set/Implicit Set Definition/Examples
- Set/Implicit Set Definition/Examples/Letters of the Alphabet