Answer:
We can use interval notation to show that a value falls between two endpoints. For example, -3≤x≤2, [-3,2], and {x∈ℝ|-3≤x≤2} all mean that x is between -3 and 2 and could be either endpoint.
Lets say you had the compound inequality [tex]5 \le x \le 7[/tex] 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 [tex]5 < x \le 7[/tex] 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 [tex]5 \le x < 7[/tex] to [5, 7)
Finally, [tex]5 < x < 7[/tex] 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.
