Finite & Infinite Intervals
Interval Notations
Two Endpoints
Note: > or < graph as open circles or ( ) in interval notation – endpoint is not included
> or < graph as closed circles or [ ] in interval notation – endpoint is included
|Set Builder Notation |Interval |Interval |
| |Notation |Type |
| { x | a < x < b} |= [a, b] |Closed |
| { x | a < x < b} |= [a,b) |closed-open |
| { x | a < x < b} |= (a, b] |open-closed |
|{ x | a < x < b} | = (a,b) |Open |
One Endpoint
Note: Parentheses ( ) are always used with [pic] or [pic]
| Set Builder Notation |Interval Notation |
| { x | x > a } |= [a, [pic]) |
| { x | x > a } |= (a, [pic]) |
| { x | x < a} |= ([pic], a] |
| { x | x < a} |= ([pic], a) |
|(all real numbers) R |= ([pic], +[pic]) |
Combining Two Intervals
Two or more intervals that do not overlap are combined by the union symbol [pic]
Example: [pic]
Notice that each interval is disjoint or has endpoints that do not overlap…
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