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This notation is my favorite for intervals.  It's just a lot simpler!

Let's look at the intervals we did with the set-builder notation:

0 is less than or equal to x < 4

x > -1

x is less than or equal to 2

x < 0 or x > 3

Let's start with the first one:

0 is less than or equal to x < 4

This is what it means;

number line showing x is greater than or equal to 0 and less than 4

So, we write it like this:

[ 0, 4 ) This is interval notation!

Use [ or ] for closed dots  less than or equal to, greater than or equal to

Use ( or ) for open dots  < , >