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

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