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Set-Builder Notation

There are two notations for writing inequalities besides the basic style

0 is less than or equal to x which is less than to 4

x is greater than -1

x is less than or equal to 2

x is less than 0 or x is greater than 3

The first one I'm going to show you is called "set-builder notation."  All you have to do on this one is take the guys we have above and put them in a bracket thing like this:

{ x | ___________ } ... the set of x such that

So, they'd be

{ x | 0 is less than or equal to x < 4 } ... the set of x such that 0 is less than or equal to x which is less than 4

{ x | x > -1 } ... the set of all x such that x is greater than -1

{ x | x is less than or equal to 2 } ... the set of x such that x is less than or equal to 2

{ x | x < 0 or x > 3 } ... the set of x such that x is less than 0 or x is greater than 3

Here's how you read it and what it means:

{ } this is set notation

You read the whole thing like...

{ x | x is less than or equal to 2} ... the set of all x such that x is less than or equal to 2

Personally, I think the next notation is a lot slicker... And the fact that I have an opinion on this makes me a royal geek.  I'm aware!

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