Example: "boxes approximately 20 kg in mass are allowed"

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

It isn"t really clear.

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

Inequalities The Number heat Interval Notation

Inequalities

With Inequalities we use:

> greater than≥ greater than or same to less than≤ 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 when we desire to include the finish value, or( ) a ring bracket as soon as we don"t

Like this:

*


Number Line

With the Number heat we attract a thick line to present the worths we room including, and:

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

Like this:


Example:

*

means every the numbers in between 0 and 20, perform not encompass 0, however do encompass 20


From 1To 2
Including 1Not consisting of 1Not including 2 including 2
Inequality:x ≥ 1 "greater than or same to"x > 1 "greater than" x "less than" x ≤ 2 "less 보다 or equal to"
Number line:
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1" width="70" height="55" />
, and not encompass 2:


Inequality:

x ≥ 1 and x

or together: 1 ≤ x

Number line:

That method up to and including $10.

And it is fair to say every prices are much more than $0.00.

As one inequality we display this as:

Price ≤ 10 and also Price > 0

In fact we could combine that into:

0 (0, 10>


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

<3, +∞)

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Example: x ≤ 2 or x >3

On the number line it looks like this:

*

And term notation looks choose this:

(-∞, 2> U (3, +∞)

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


Note: be careful with inequalities like that one. Don"t try to join it into one inequality:

2 ≥ x > 3

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wrong!

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

Union and also Intersection

We simply saw exactly how to sign up with two sets making use of "Union" (and the prize ∪).

There is likewise "Intersection" which method "has to be in both". Think "where carry out they overlap?".

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The Intersection price is an upside under "U" prefer this:


Example: (-∞, 6> ∩ (1, ∞)

The very first interval goes up to (and including) 6

The 2nd interval goes native (but no including) 1 onwards.





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The Intersection (or overlap) of those 2 sets goes native 1 come 6 (not including 1, including 6):

(1, 6>




Footnote: Geometry, Algebra and Sets

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