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.

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

Inequalities The Number line Interval Notation


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:



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:


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


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: