Any non-periodic infinite decimal number is called an *irrational numbe*r.

Example:

The numbers 2,232332333 … , √2, √3, π, ar*e i*rrational 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 i

*s*ca

*l*led the

*interval*. The number

*s a*a

*nd*b are called

*the ends of the interva*l.

If the ends a

**and**

**b belong to the interval it is called closed interval and is denoted by:**

**If the ends a**

**[а,b] = {x ∈ R | a ≤ x ≤ b}***nd*

*a**b do not belong to the interval, it is an open interval and is denoted by:*

(а, b) = {x ∈ R | a <x <b}(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 –