Question

What is interval notation? Could you please give an example?

Answer 1

Lets say you had the compound inequality
`5 \le x \le 7` which describes x being anything between 5 and 7, including both endpoints. This is the interval from 5 to 7.

To write this in interval notation, we would write [5, 7]

The square brackets mean "include the endpoint"

If we had something like
`5 < x \le 7` then we would write (5, 7]. Note how I'm using a curved parenthesis to exclude the endpoint 5.

If we exclude 7, but keep 5, then we will go from
`5 \le x < 7` to [5, 7)

Finally,
`5 < x < 7` converts to (5,7) and we're excluding both endpoints. Unfortunately this last example is identical to ordered pair (x,y) point notation. So be sure not to mix up those two concepts.

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In short, interval notation is where we list the endpoints of the interval, and use parenthesis or brackets to exclude or include the endpoint.

Answer 2

We can use interval notation to show that a value falls between two endpoints. For example, -3≤x≤2, [-3,2], and x∈ℝ all mean that x is between -3 and 2 and could be either endpoint.