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.

You are watching: What does upside down u mean in math

Let"s see exactly how to be an accurate about this in every of three popular methods:

Inequalities The Number line Interval Notation


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:



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:


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>

Example: x higher than, or same to, 3:

<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


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?".

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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: