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
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"tLike this:
Number Line
With the Number heat we attract a thick line to show the worths we space including, and:
a filledin 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 1   To 2 
 Including 1  Not including 1   Not 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>
Example: x higher than, or same to, 3: <3, +∞)
Example: x ≤ 2 or x >3On 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 IntersectionWe 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 SetsYou might not have actually noticed this ... Yet we have actually actually to be using:

