Example: "boxes up to 20 kg in mass room allowed"

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

It isn"t yes, really clear.

You are watching: What does the upside down u mean


Let"s see just how to be precise about this in each of three well-known methods:

Inequalities The Number line Interval Notation

Inequalities

With Inequalities we use:

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

Like this:


Interval Notation

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

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

Like this:

*


Number Line

With the Number line we draw a thick heat to display the values we space including, and:

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

Like this:


Example:

*

means every the numbers between 0 and 20, perform not include 0, yet do incorporate 20


From 1To 2
Including 1Not consisting of 1Not consisting of 2 including 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 not incorporate 2:


Inequality:

x ≥ 1 and also x

or together: 1 ≤ x

Number line:

That way up to and also including $10.

And the is fair to say all prices are more than $0.00.

As one inequality we show this as:

Price ≤ 10 and also Price > 0

In reality we could integrate that into:

0 (0, 10>


Example: x better than, or equal to, 3:

<3, +∞)

*


Example: x ≤ 2 or x >3

On the number line it looks favor this:

*

And interval notation looks choose this:

(-∞, 2> U (3, +∞)

We offered a "U" to typical Union (the joining with each other of 2 sets).


Note: be mindful with inequalities prefer that one. Don"t shot to sign up with it right into one inequality:

2 ≥ x > 3

*
wrong!

that doesn"t make sense (you can"t be much less than 2 and greater 보다 3 at the exact same time).

Union and also Intersection

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

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

See more: How Many Protons Does Fluorine Have, Fluoride, Fluorine Chemistry

The Intersection prize is an upside under "U" favor this:


Example: (-∞, 6> ∩ (1, ∞)

The first interval goes as much as (and including) 6

The 2nd interval goes indigenous (but not including) 1 onwards.





*

The Intersection (or overlap) that those 2 sets goes from 1 to 6 (not consisting of 1, consisting of 6):

(1, 6>




Footnote: Geometry, Algebra and also Sets

You might not have noticed this ... However we have actually actually been using: