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 inclusivityorexclusivity,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

InclusiveExclusive
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 NotationCloseddot(filledincompletely)Closed dot (filled in completely)Opendot(leftemptyinthemiddle)Open dot (left empty in the middle)
Number Line Notation Diagrams:

Infinity

ArrowsonanumberlineindicateinfinityArrows 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