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Questions and Answers
Intervals are always written _____
Intervals are always written _____
left to right, smallest to biggest
[a, b] means ____ and is called ____ and endpoints are _____
[a, b] means ____ and is called ____ and endpoints are _____
{a (less than or equal to) x (less than or equal to) b}, closed interval, included
(a, b) means ____ and is called ____ and endpoints are _____
(a, b) means ____ and is called ____ and endpoints are _____
{a < x < b}, open interval, not included
[a, b) means ____ and is called ____
[a, b) means ____ and is called ____
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Unbounded intervals: x (less than or equal to) 5 --> _____
Unbounded intervals: x (less than or equal to) 5 --> _____
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_____ replaces V (or) and _____ replaces ^ (and) when writing _______
_____ replaces V (or) and _____ replaces ^ (and) when writing _______
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Study Notes
Interval Notation Basics
- Intervals are expressed left to right, from smallest to largest value.
Types of Intervals
- Closed interval [a, b]: Includes endpoints; defined as {a ≤ x ≤ b}.
- Open interval (a, b): Does not include endpoints; defined as {a < x < b}.
- Half-open interval [a, b): Includes the left endpoint but not the right; defined as {a ≤ x < b}.
Unbounded Intervals
- An unbounded interval such as x ≤ 5 is represented as [5, ∞).
Set Operations in Intervals
- Union (U) is used to denote "or" between intervals.
- Intersection (∩, upside down U) is used to denote "and" between intervals.
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