Interval Notation
Definition: A notation for representing an interval as a pair of numbers. The numbers are the endpoints of the interval. Parentheses and/or brackets are used to show whether the endpoints are excluded or included. For example, [3, 8) is the interval of real numbers between 3 and 8, including 3 and excluding 8.
Interval notation rights the solution of the equation in an interval, or representation of a segment of values along the number line.
For example the solution is 2<x<10. On a number line the solution looks like this:
For example the solution is 2<x<10. On a number line the solution looks like this:
The solution is able to be any value along the blue line. There are circles around 2 and 10 because the solution is not equal to either value. If the solution included 2 or 10 then it would have been colored in, and the notation would have a bracket versus a parentheses. For this example the solution in interval notation would be (2,10). As the least value 2 is placed on the left, while ten the largest value is place to the right.
When the solution describes in comparison to one value an infinity symbol will be used. If the solution is x<n, then as n is the lowest value that x is associated with the interval notation would have a positive infinity symbol to the right. If the solution is x>n, then the opposite would be true.
If a solution with two value, similar to the first example, does not overlap on the number line, then they are written as separate solutions in interval notation with the symbol ‘U’ in-between them.
When the solution describes in comparison to one value an infinity symbol will be used. If the solution is x<n, then as n is the lowest value that x is associated with the interval notation would have a positive infinity symbol to the right. If the solution is x>n, then the opposite would be true.
If a solution with two value, similar to the first example, does not overlap on the number line, then they are written as separate solutions in interval notation with the symbol ‘U’ in-between them.