﻿ Intervals and straight lines. What they are and how they are represented

# Intervals and straight lines. What they are and how they are represented, step by step

Do you know what intervals and straight are? When are they used? How are they represented? Now I’m going to explain to you what intervals and straight lines are. I will explain to you what types of intervals and straight lines there are and what each one means.

## What is an interval

An interval is a set of real numbers, a range of values, which is limited by two extremes a and b, where a and b are real numbers.

It may be open at both ends, meaning that those ends are not included in the interval, or may be closed at both ends, meaning that those ends are included.

They may also be open at one end and closed at the other.

To represent that an extreme is not included in the interval parentheses are used () and to represent that it is included the square brackets are used [].

We’re going to see each of them.

## Types of intervals

### Open interval

It’s called open interval:

Al set of real numbers between a and b, but a and b are not included.

Covers all real numbers greater than a and less than b, which is what the following expression means:

The symbol / means “such that”.

Represented on the actual line, the interval is represented as follows:

As you can see, extremes a and b are empty, as they are not included in the interval.

### Closed interval

A closed interval:

This is the set of real numbers between a and b, where a and b are also included.

It includes all real numbers greater than or equal to a and less than or equal to b and is written like this:

When the equal sign appears in the inequality symbol, the end is included in the interval.

And it would be represented on the line as follows:

The ends a and b are filled, as they belong to the interval.

### Half-open interval on the left

A half-open interval on the left:

This is the set of real numbers between a and b, where a is not included and b is included.

Covers all real numbers greater than and less than or equal to b:

When representing this interval, the end a will be empty and the end b will be filled:

### Half-open interval on the right

A half-open interval on the right:

This is the set of real numbers between a and b, where a is included and b is not included. It includes all real numbers greater than or equal to a and less than b:

And that’s how it’s represented:

## What is a straight line

Have you ever wondered what a straight line is?

Intervals that start at less infinity or end at infinity are called straight line.

Therefore, straight lines are delimited at one end only, since the opposite end begins at less infinity or ends at infinity, depending on the direction of the straight line.

Straight linea can be open or closed at the end that delimits them. The end that ends in infinity or begins in less infinity is always open (the parenthesis will be used to open or close).

## Types of straight line

Let’s see the different types of straight lines:

### Straight line opened on the right

A straight lineopened on the right:

The range of values from the least infinite, to the extreme a, but not including it.

Covers numbers less than a:

And it is represented as follows:

Where the point a is empty.

### Straight line closed by the right

A straight line closed on the right:

Values ranging from the least infinite to extreme a, including extreme a are included.

Covers values less than or equal to:

In this case, the point a is filled because it also belongs to the ray:

### Straight line opened on the left

A straight line opened on the left:

Part from extreme a, which is not included and ends in infinity.

Thus understands values that are greater than a:

And it is represented as follows:

### Sstraight line closed by the left

The straight line closed on the left:

The range of values from point a, included, to infnito-

The range of values from point a, included, to infnito-

O in other words, values that are greater than or equal to a:

It is represented as follows:

## What are intervals and straight lines used for?

Intervals and straight lines are used to represent ranges of values such as the domain or the image of a function or the result of a mismatch.