Real numbers

Any non-periodic infinite decimal number is called an irrational number.
Example:
The numbers 2,232332333 … , √2, √3, π, are irrational numbers.

The set of irrational numbers is denoted by I
The set R = Q ⋃ I is called the set of real numbers.


1. INTERVAL

Let a, b ∈ R. The set of all real numbers between the numbers a and b is called the interval. The numbers a and b are called the ends of the interval.
If the ends a and b belong to the interval it is called closed interval and is denoted by:
[а,b] = {x ∈ R | a ≤ x ≤ b}
If the ends a and b do not belong to the interval, it is an open interval and is denoted by:
(а, b) = {x ∈ R | a <x <b}

The following intervals are also used:

[a , b) = { x ∈ R | a ≤ x < b }
(a , b] = {x ∈ R | a <x ≤ b}
[a , +∞) = { x ∈ R | x ≥ a }
(a , +∞] = {x ∈ R | x ≥ a}
(-∞, a) = {x ∈ R | x <a}
(-∞, a) = {x ∈ R | x <a}
(-∞, + ∞) = {x ∈ R}

– Real numbers –

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