Interval Notation: A Comprehensive Guide to Representing Real Numbers within Ranges

interval notation

-an expression that uses inequalities to describe subsets of real numbers-[x,y] or (x,y)

Interval notation is a way of representing a set of real numbers within a specific range or interval in a concise and organized way. It consists of enclosing the range of numbers within brackets [ ] and separating the endpoints of the interval by a comma. There are four types of interval notation:

1. Open interval notation: (a, b)
This notation denotes an interval that does not include its endpoints a and b, but all the real numbers within it. For example, (3,7) denotes the interval of real numbers between 3 and 7, excluding 3 and 7.

2. Closed interval notation: [a, b]
This notation denotes an interval that includes both endpoints a and b as well as all the real numbers between them. For example, [2,6] denotes the interval of real numbers between 2 and 6, including 2 and 6.

3. Half-open interval notation: [a, b) or (a, b]
This notation denotes an interval that includes one endpoint and excludes the other. For example, [1,5) denotes the interval of real numbers greater than or equal to 1 and less than 5, including 1 but excluding 5.

4. Empty interval notation: Ø
This notation denotes an interval with no real numbers in between, or the empty set. For example, (4,3) or [5,3) would denote an empty interval as there are no real numbers that are greater than 4 and less than 3 or greater than or equal to 5 and less than 3.

It’s important to note that in interval notation, the endpoint values are not repeated, as opposed to using brackets or parenthesis in a standard number line.

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