### Example: "boxes as much as 20 kg in mass space allowed"

If your box is exactly 20 kg ... Will certainly that be enabled or not?

It isn"t really clear.

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Inequalities The Number line Interval Notation

## Inequalities

With Inequalities us use:

> greater than≥ higher than or same to much less than≤ much less than or equal to

Like this:

## Interval Notation

In "Interval Notation" we simply write the beginning and also ending number of the interval, and also use:

< > a square bracket when we desire to include the end value, or( ) a round bracket as soon as we don"t

Like this:

## Number Line

With the Number heat we attract a thick line to show the worths we space including, and:

a filled-in circle as soon as we want to incorporate the end value, oran open up circle when we don"t

Like this:

Example:

means all the numbers in between 0 and 20, carry out not encompass 0, yet do include 20

From 1To 2
Including 1Not including 1Not including 2 consisting of 2
Inequality:x ≥ 1 "greater 보다 or equal to"x > 1 "greater than" x "less than" x ≤ 2 "less 보다 or equal to"
Number line:
1" width="70" height="55" />
, and also not include 2:

Inequality:

x ≥ 1 and also x

or together: 1 ≤ x

Number line:

That method up to and also including \$10.

And that is same to say all prices are more than \$0.00.

As one inequality we display this as:

Price ≤ 10 and also Price > 0

In fact we could incorporate that into:

0 (0, 10>

<3, +∞)

### Example: x ≤ 2 or x >3

On the number line it looks choose this:

And expression notation looks prefer this:

(-∞, 2> U (3, +∞)

We provided a "U" to mean Union (the joining together of two sets).

 Note: be cautious with inequalities choose that one. Don"t try to sign up with it right into one inequality: 2 ≥ x > 3 wrong!that doesn"t make feeling (you can"t be much less than 2 and also greater than 3 in ~ the same time).

## Union and Intersection

We just saw how to join two sets utilizing "Union" (and the prize ∪).

There is also "Intersection" which way "has to be in both". Think "where execute they overlap?".

See more: What Characteristics Do Geologists Use To Classify Metamorphic Rocks

The Intersection price is one upside under "U" prefer this:

### Example: (-∞, 6> ∩ (1, ∞)

The an initial interval goes up to (and including) 6

The second interval goes native (but no including) 1 onwards.

The Intersection (or overlap) that those two sets goes native 1 to 6 (not consisting of 1, consisting of 6):

(1, 6>

### Footnote: Geometry, Algebra and also Sets

You might not have actually noticed this ... Yet we have actually actually to be using: