In mathematics, numbers are usually divided into different groups where each one has specific characteristics that differentiate it from the rest. One of these numerical sets are the** ordinal numbers**whose use is very common in various fields to indicate the position or relative order of something.

On the other hand, there are the cardinal numbers, which are used to **count the elements of a certain group**. In this topic we will focus especially on understanding what ordinal numbers are, their use, characteristics and the difference between them and cardinal numbers.

## Meaning and concept of ordinal numbers in mathematics

In mathematics, an ordinal number (set theory) is understood as that whole number used to indicate the **relative order or position of an element in a series** or sequence. Unlike cardinal numbers, ordinals are used to indicate the position of an element in relation to the rest.

In general, despite being a natural number, an ordinal number is represented by a letter or number followed by a suffix that indicates its position in the series, for example, **first (1st), second (2nd), third (3rd)**etc.

Ordinal numbers are considered important in different areas, such as in **economics, biology, statistics, physics and chemistry**. They are also very important in everyday language to refer to the position of something in a series.

## What are ordinal numbers used for?

Ordinal numbers have various applications and **are used to indicate the order of an element in series or sequence**. Some of the main applications or uses given to ordinal numbers are the following:

- In everyday language: Usually used to refer to serial positions of someone or something. Some very common examples are in the
**careers, on a to-do list, a ranking**among others. - In statistics: in this area of study ordinal numbers are often used to order data and establish hierarchies or rankings. For example, it tends to be used for
**rank countries according to their human development index**order products according to their level of sales, and many more examples. - In biology: it is very common to see the use of ordinal numbers to indicate the
**position of an organism in a food chain**. As it can also be used for a taxonomic classification or other areas of biology that require it. - In physics and chemistry: these types of numbers tend to be used to indicate the
**element positions on the periodic table**. - In mathematics: in the
**set theory**To define the different types of infinities, the use of ordinal numbers is very natural. As well as in theory to define transfinite ordinal numbers or in geometry, to define spatial dimensions or coordinate systems.

In general, ordinal numbers **are a valuable tool in various disciplines** to define classifications, orders or rankings.

## What are the characteristics or conditions of ordinal numbers?

Ordinal numbers have a specific function for their use, and differ from the various types of sets of numbers existing in mathematics. It is because of that **have certain characteristics and/or conditions** that they must comply with, such as the following:

- These numbers indicate the
**relative position of an element within a series**or sequence. - They are represented through
**a number followed by a suffix**that indicates its position in the series, a word or a letter. For example, first (1st), second (2nd), third (3rd), etc. - These numbers
**cannot be subjected to mathematical operations**like adding, subtracting, multiplying, or dividing, just like we would with cardinal numbers. - In certain languages, ordinal numbers
**have gender and number**and are usually adjusted according to the noun to which they refer. - In mathematics, ordinal numbers
**have a pecking order**used to define different types of infinities and transfinite numbers.

## What is the difference between cardinal and ordinal numbers?

The main difference that can be found between the **ordinal numbers and cardinals** is that, the latter indicate the number of elements in a set. While, ordinal numbers indicate the relative position of any element within a series.

On the other hand, the cardinal numbers are usually used to **count the number of elements in a group or set**. An example of this is if we count the pencils that are in a case and there are 10 pencils, we say that there are “ten” pencils.

These numbers are also used to perform various mathematical operations, such as the **addition, subtraction, division and multiplication**.

On the other hand, ordinal numbers are used to indicate the relative position of something or someone in a sequence or series. Like, for example, if we are in a marathon or race, and we finish in second place, we can say that **we have arrived in the “second” position**.

In this way, ordinal numbers are used to **order or classify elements hierarchically **in a series or sequence.

In short, it is understood that **an ordinal number indicates the position of an element**while a cardinal number indicates the number of elements.

## Examples of ordinal numbers in mathematics

There are several examples in everyday life where ordinal numbers are used, either in **educational areas, sciences or other activities**. For this reason, we will describe some examples of its use below:

Example 1: **In the educational area **ordinal numbers are often used to indicate which grade students are advancing to or in which grade they are in. These range from the first grade of primary school, followed by the second grade of primary school, and in this way, up to the sixth or ninth grade, depending on the country and its educational standards.

Example 2: **In the televised series “Doctor Who”**, use ordinal numbers to list the incarnations of the protagonist. We can appreciate these when they use the terms “Ninth Doctor” or “Tenth Doctor” in the series, which indicate reincarnation number nine (9) and ten (10).

Example 3: When asked the **order of children to a large family**, generally, is transmitted using the ordinal numbers. This would indicate that each member or child of the family would represent a different ordinal number, in this way: the first child, second child, third child.

We can conclude that, the ordinal numbers **They are a fundamental and essential tool** both in mathematics and in everyday life to represent the positions or places of an element in a sequence. These numbers allow us to organize or order anything or anyone in different contexts, beyond just professional mathematics or science.