Presentation Transcript
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 .