Data

Data is information that may be measured or described. It is classified into the following categories: numbers, texts, infographics, images, audios, and videos.

 

Numbers

 

 

We are all aware that we must deal with numbers on a daily basis, regardless of our interests or sector of employment.  Furthermore, we cannot deny that in this day and age, there is no such thing as mathematics or psychology being studied for the purpose of studying them. 

 

We must recognize that the emphasis is on application, better decision-making, and attempting to predict what the future may hold.  This environment necessitates the possession of a diversified skill set by experts working in several industries.  In most cases, it necessitates a grasp and implementation of fundamental principles from other disciplines.

 

To be more specific, a psychologist may not be as effective as he may be if he lacks, for example, basic computer abilities, a geneticist who lacks basic statistical understanding, or a student who wishes to pursue a career in finance but lacks basic mathematical knowledge.  The topic ‘Real Numbers’ covers the number system as well as other fundamentals such as determining the Least Common Multiple and Highest Common Factor of the given amounts.

 

Let us look at the system of numbers or numerical values to obtain a better understanding of this data type.

We will first examine how the number system evolved over time, followed by some of the important algebraic features of real numbers.

 

Natural Numbers

 

 

First, we have counting numbers.  These are also known as Natural numbers and are indicated by the symbol ‘N’.  These are the results of adding one to the previous number.  In other words, if we know the first element, we can get the subsequent elements by adding 1 to the consecutive elements.  That is, we can have an infinite number, an innumerable number, or a huge number of them.  Because natural numbers are limitless, we prefer to express them as a set.

 

A set is a collection of well-defined items.  Each individual object is also known as an element of that specific collection.  It is important to note that the concept of set can be used to describe both an infinite and a finite number of components.  The vowels a, e, i, o, and u can be written as a set, which is a simple example of a finite number of elements.  In general, the set of natural numbers is denoted as

N = {1, 2,3,…………………….}

As we examine other sets, we will notice that the set of natural numbers has a lot of setbacks.

 

Whole Numbers

 

 

We notice that there is no zero in the natural numbers.  When we consider the set of whole numbers, we may compensate for this weakness.  The set of whole numbers is symbolised by the letter ‘W’ and is written as

W = (0, 1, 2, 3,………………….}

 

Integers

 

 

The set of whole numbers also does not meet all of our requirements because it does not include negative numbers such as -2, -7, and so on.  To address this problem, a set of elements known as Integers was created.  The symbol “I” represents this set. It is depicted as

I = {………-3, -2, -1, 0, 1, 2, 3,………}

This set is clearly superior to natural and whole numbers in that it caters to a larger audience than the other number systems discussed above.

 

Rational Numbers

 

 

Although the set of integers serves a larger audience, it is insufficient.  This shortcoming has resulted in the development of Rational numbers.

 

Rational numbers have the form p/q, where p and q are integers and q is greater than zero.  Examples of rational numbers include 2/3 and -5/4.  The set of rational numbers is represented by Q and is commonly written as

Q = {………, -2/5, -1/4, 0/1, 3/5, 6/7, 7/8,………}

If we consider any of the elements in the set of rational numbers, say -2/5, we find that the quotient is -0.4. Similarly, when 7/8 is used, the quotient is 0.875.  The decimal part ends in each of these circumstances.  We understand that the division procedure is coming to a conclusion by terminating.  Consider the element 6/7 in the same set.  The quotient for this number is 0.857142857142………  In this example, the decimal component (i) is not terminating and (ii) is repeating.

 

However, there are times when decimals do not terminate or repeat.  Consider the following example: 65/67.  The quotient is in the form 0.970149253………  The decimal does not terminate or repeat in this fraction.  Numbers with non-terminating and non-repeating decimals are classified as irrational numbers.

 

Real Numbers

 

 

The real numbers are made up of all of the number sets we’ve seen so far.  Real numbers are also insufficient in that they do not include a quantity that is the square root of a negative number.  To deal with large quantities, one must go to complex numbers.

 

Author

Srilakshmi K, MSc

Co-Founder & CEO, Iconxt Interactive