[Mathematics] Type and notation of interval

In mathematics, a (real) interval is a set of real numbers lying between two numbers, we used to see something like this:

x < 4

it means x is smaller than 4.

-2 ≤ x ≤ 3

and this mean x is greater or equal to -2 and less than or equal to 3.

Types of the interval :

• close-interval
• open-interval, doesn't not 
• half-interval
• infinite interval 

Close interval

we use the notation [ or ] to represent the closed side

[-2,3] means -2 ≤ x ≤ 3

Open interval

we use the notation ( or ) to represent the open side

(-16,-9) means -16 < x < -9

Half interval

you would have both open side and close side in the interval.

[-7,2) means -7 ≤ x < 2

Infinite interval

For infinite interval, the ∞ sign is used.

(1,∞ ) mean x>1

More usage and example:

http://www.csgnetwork.com/directintervalcalc.html

Remarks

Sometimes we use the union notation ⋃ to join two interval"

(-∞,1)⋃[∞,2)

(-∞,1) means interval x<1 and [∞,2) means interval x≥ 2.

(-∞,1)⋃(∞,2) is equivalent to x<1 or x≥ 2.

and intersect notation ∩ to get the collection of values in both interval:

(-∞,2)∩[1,3)

(-∞,2) means interval x<2 and [1,3) means interval 1≤x<3.

(-∞,2)∩[1,3) is equivalent to 1≤x<2.

Reference:

https://en.wikipedia.org/wiki/Interval_(mathematics)

https://wikidiff.com/interval/range