Interval Notation

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Interesting Interval Notation : 

Interesting Interval Notation

You are already familiar with expressing intervals algebraically… : 

You are already familiar with expressing intervals algebraically…

And you’re probablyfamiliar with theirnumberline representations… : 

And you’re probablyfamiliar with theirnumberline representations…

Slide 7: 

3

Slide 8: 

-5 8

Slide 9: 

4

But, there is another way to represent intervals. : 

But, there is another way to represent intervals.

Start by looking at the numberline representation. : 

Start by looking at the numberline representation.

If you see an open circle : 

If you see an open circle 3

If you see an open circle : 

If you see an open circle 3 Replace it with a parenthesis: ( goes on the left ) goes on the right ) 3

If you see a solid circle : 

If you see a solid circle 4

If you see a solid circle : 

If you see a solid circle 4 Replace it with a square bracket: [ goes on the left ] goes on the right [ 4

They can even be combined… : 

They can even be combined… -5 8 -5 8 [ )

That’s nice, but I haven’t used numberlines since elementary school… : 

That’s nice, but I haven’t used numberlines since elementary school…

There’s more.We can extend this idea to represent an interval compactly. : 

There’s more.We can extend this idea to represent an interval compactly.

Put the lowest value of the interval on the left, and the highest on the right. Separate them with a comma. : 

Put the lowest value of the interval on the left, and the highest on the right. Separate them with a comma.

Put the lowest value of the interval on the left, and the highest on the right. Separate them with a comma. : 

Put the lowest value of the interval on the left, and the highest on the right. Separate them with a comma. 5, 8

Use square brackets if endpoint is included.Use parenthesis if endpoint is not included. : 

Use square brackets if endpoint is included.Use parenthesis if endpoint is not included. [5,8)

But what if the interval goes to infinity? : 

But what if the interval goes to infinity?

Since we can’t “reach” infinity, use parenthesis. : 

Since we can’t “reach” infinity, use parenthesis.

Since we can’t “reach” infinity, use parenthesis. : 

Since we can’t “reach” infinity, use parenthesis. (-, 3)

Slide 25: 

[4, )

TheBig Ideas : 

TheBig Ideas

TheBig Ideas : 

TheBig Ideas Use square brackets if the endpoint is included

TheBig Ideas : 

TheBig Ideas Use square brackets if the endpoint is included Use parenthesis if the endpoint is excluded, or if the interval goes to .