How can you figure out the interval notation if you are given the Set Builder notation or the Number Line?

Answer 1

The best way to do this is to draw a number line graph by using the set builder notation. Typically, set builder notation gives some sort of inequality. Simply draw this inequality on a number line. Use solid circles if the value is included and an open circle if the value is not included. Remember that interval notation is written left to right from least to greatest. Label your number line at the far left as -oo (negative infinity) and the far right side as +oo (positive infinity). Now, work your way from left to right (least to greatest).

Here are some rules for interval notation:

1) Use a parentheses when the solution set includes all values up to this number, but does not include the number:

x > 6 in interval notation is (6, + oo)

2) Use a bracket when the solution set includes all values up this number and also includes this number.

[6, 10) means all values between 6 and 10, while including 6

3) The comma between the two values means all values between.

4) Always use a parentheses for the far left -oo and the far right +oo, since infinity is a symbol not a value.

(-oo, +oo) means all real numbers between negative infinity and positive infinity.

Hope that helps.