Interval notation
The next topic that we have to discuss is the idea of interval notation. Interval notation is some very pleasant shorthand for inequalities & will be utilized extensively. The best way to explain interval notation is the following table. There are three columns in the table. Each row has an inequality, a graph representing the inequality & lastly the interval notation for the given inequality.
Recall that a bracket, "[" or "]", means that we involved the endpoint while a parenthesis, "(" or ")", means we don't involved the endpoint.
Now, along with the first four inequalities within the table the interval notation is actually nothing more than the graph without the number line on it. With the last four inequalities the interval notation is approximately the graph, except we have to add in suitable infinity to ensure we get the accurate portion of the number line. Also notice that infinities never get a bracket. They only acquire a parenthesis.