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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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
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
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
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:|
x ≥ 1 and also x
or together: 1 ≤ x
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:
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):
Footnote: Geometry, Algebra and also Sets
You might not have actually noticed this ... Yet we have actually actually to be using: