Mathematicians have designed ways to identify how a given number differs from another. As with other notions in any science, the different types of numbers often seem to overlap. Given that the real numbers include all rational numbers as well as integers, they have few similar properties, such as using whole numbers.

## Real Numbers Vs. Integers

The major distinction between Real numbers and IntegersĀ is that real numbers are a general category of numbers, while integers are a subset characterized by the fact that they are mainly concerned with whole numbers (negative and positive).

Real numbers include integers, rational numbers, irrational numbers, natural numbers, and whole numbers, whereas integers only include whole numbers and their negatives. Thus, real numbers comprise decimal and fractional numbers. Integers, on the other hand, must always be whole numbers (and their negatives). Fractions and decimals are not included in integers.

## Real Numbers

There is nothing more important in the world of numbers than real numbers. Their contribution to the development of mathematics cannot be overstated. You can think of any real number (excluding an imaginary number) that comes to mind. Negative, positive, fractional, irrational, or even 0 are all possibilities.

All of the subsets of the real number system may be represented on the real number line: integers; rational; irrational; natural; and entire. Descartes invented the word “real” to denote polynomial roots in order to differentiate them from imaginary numbers.

Allowable values include fractions Because of their uniqueness, they are distinguished from the integers. The uncountable infinite is formed by real numbers. Between the points 0 and 1, there are an unlimited amount of real numbers on the number line.

*Both “R” and “R” are used to denote the whole set of real numbers.*

## Integers

The Real number system contains the Integer number system as a subset. However, this does not imply that all integers are real numbers. A number can only be an integer if it is a whole number as well as its negative. Counting numbers, such as 0, 1, 2, 3, etc., are included in the concept of whole numbers.

This system is special in that it does not include fractional or decimal numbers. The origins of real numbers are a fascinating topic in and of themselves. Arbermouth Holst experimented with rabbits and elephants in the year 1563.

He then devised this number system to aid him in this endeavor. An older Latin term, “integer”, has given rise to the modern English word “integer”, which means “whole” or “intact” in Latin. The non-fractional character of this system is bolstered by this fact.

Integers, unlike real numbers, have a set of countable infinite numbers. There are no integers between the points 0 and 1 on the real number line. The set of all integers is symbolized by the letter “Z”.

## Difference Between Real Numbers and Integers

- Real numbers include all integers, rational numbers, irrational numbers, natural numbers, and entire numbers. Integers can only be whole integers or their negatives.
- Real numbers may contain fractions and decimals, but not integers.
- Using the real number line, it is possible to differentiate between the two systems of number. An actual number may be found at any of the points on this line. Integers consist of whole integers and their corresponding negative numbers on a number line.
- There exist infinite sets in each of these number systems by their own nature. Real and Integer numbers, on the other hand, constitute a countable and an uncountable infinity.
- “R” or “R” is the abbreviation for the set of all real numbers. Integers are represented as “Z” in this context.

## Conclusion

With the aid of integers, we can employ mathematics in our daily lives more effectively. Positive and negative values, for example, represent profits and losses in the context of business deals.

Using the term “real” indicates that real numbers are not imaginary numbers. With imaginary numbers, they become complex numbers.

Real numbers include integers, rational and irrational numbers, as well as whole numbers, and other naturally occurring numeric types. Integers can only be whole integers or their negatives.

The omission of fractional numbers in integers makes them distinct from real numbers. Real numbers enable fractions and decimals.