# Mathematics 1010 online

## Intervals

Intervals are chunks of the real line. Specifically we define for real numbers and :

• : the set of all numbers satisfying .
• : the set of all numbers satisfying .

• : the set of all numbers satisfying .

• : the set of all numbers satisfying .

So, for example, the interval is the set of all numbers greater than or equal to and less than . The numbers , , and are in the interval, the numbers , and are not.

The notation may be a little confusing, but just remember that square brackets mean the end point is included, and round parentheses mean it's excluded. If both end points are included the interval is said to be closed, if they are both excluded it's said to be open. If one is included and the other excluded the interval is half open (or half closed, depending on your preference).

Now things get a little murky because the above notation is also used with replaced with or replaced with (and only round parentheses at that end). This means that the interval is unlimited on the right or left, respectively.

For example the notation is a fancy way of describing the set of all numbers greater than , and means the set of all number less than or equal to . The set of all real numbers can be expressed as .