12-00: Interval Notation
Sets of real numbers can be described in a variety of ways
Various Notations
3 Main Notations
Set builder notation
- e.g. {x E R/-3 ≤ x ≤ 5}
Number line
e.g.
Includes all numbers between -3 and 5
==Interval notation==
- e.g. x E [-3, 5]
- All of these notations represent the same thing
Interval Notation
A notation for representing an interval as a pair of numbers
There are many things which are used that represent inclusivity or exclusivity, which is important to note when using any of the above notations
- Inclusivity: the end point is included
- Exclusivity: the end point is excluded
Inclusive and Exclusive Attributes
| Inclusive | Exclusive | |
|---|---|---|
| Interval Notation | ==Square brackets [ ]== | ==Round brackets ( )== |
| Set Builder Notation | @@≤ or ≥ (less than equal to, greater than equal to)@@ | @@< or > (less than or greater than)@@ |
| Number Line Notation | Closed dot (filled in completely) | Open dot (left empty in the middle) |
Number Line Notation Diagrams:
Infinity
Arrows on a number line indicate infinity
If it is facing left, then it is negative infinity:
If it is facing right, then it is positive infinity:
- Infinity is always exclusive, you must always exclude both positive and negative infinity (so use round brackets, < or >, and of course an arrow head symbolizes infinity as discussed above)
Solid lines or not clearly defined points
- a solid line (or a point on a line that doesn’t have any circle, whether it’s filled in or not) is inclusive