Intervals

Interval: all the numbers between two given numbers. Example: all the numbers between 1 and 6 is an interval. All real numbers (whole numbers, rational numbers, and irrational numbers) that lie between two values.

Inequalities We use the following: When do you include the numbers at each end? Whenever you have greater than or EQUAL to or less than or EQUAL to you include the number at the end. Otherwise you do not.

Interval notation In "Interval Notation" we just write the beginning and ending numbers of the interval, and use: [ ] closed brackets is when we want to include the end value ] [ open brackets is when we do not want to include a number. Example [2, 5[ means that 2 is included in the interval but 5 does not. On a number line it would appear like this: _- 1_______0_______1________2_______3________4________5 __ 

Intervals and line segments With the number line we draw a thick line to show the values we are including, and: a filled-in circle when we want to include the end value an open circle when we do not Example:

Infinity ∞ Infinity is not a real number, therefore it just means in this case “continuing on…” Note for this class, we would write it as [3, +∞[ In more advanced math courses (Cegep/University) will you represent it with round brackets.

Infinite ends There are four possible infinite ends: Interval Inequality ]a, +∞[ x > a “greater than a” [a, +∞[ x ≥ a “ greater than or equal to a” ]-∞, a[ x < a “less than a” ]-∞, a] x ≤ a “less than or equal to a” We could even show no limits by using this notation: ]-∞ + ∞[

Set Builder Notation Set-builder notation is a mathematical shorthand for precisely stating all numbers of a specific set that possess a specific property.

Homework Workbook pages 24 and 25!