Difference between Real Numbers and Integers 

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Mathematicians have occurred systems to specify exactly how a certain number is different from another. As with other concepts, number categories overlap. Since real numbers include all rational numbers like the integers, castle share similar characteristics such as the use of totality numbers and also being plotted on the number line. Hence, the an essential difference is that real numbers is a general category while integers is a subset i beg your pardon is characterized overall numbers which deserve to have an adverse properties.

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What are genuine Numbers?

Real numbers room the worths you can uncover on the number heat which is commonly expressed together a geometric horizontal line wherein a chosen point functions as the “origin”. Those that fall on the right side are labeled as hopeful while those ~ above the left space negative. The description “real” to be presented through Rene Descartes, a famous mathematician and philosopher in the 17th century. He specifically set the difference between Polynomials’ real roots and their imagine roots.

Real numbers incorporate whole, integers, natural, rational, and also irrational numbers:

Whole numbers

Whole numbers are positive numbers which have no fractional parts nor decimal points together they represent entirety objects without fragments or pieces.


Integers are entirety numbers which incorporate the an unfavorable side of the number line.

Natural numbers

Also well-known as counting numbers, organic numbers are like totality numbers however zero is not included as nothing have the right to be essentially counted as “0”.

Rational numbers

Regarding that origins, Pythagoras, the old Greek mathematician proclaimed the all numbers to be rational. Reasonable numbers are the quotients or the fountain of two integers. Where p and also q room both integers and q is not equivalent to zero, p/q is a reasonable number. Because that instance, 3/5 is a rational number however 3/0 is not.

Irrational numbers

Pythagoras’ student, Hippasus disagreed that all numbers were rational. Through geometry, he showed that part numbers were irrational. For instance, the square source of two, i beg your pardon is 1.41 cannot be expressed together a fraction; hence, that is irrational. Unfortunately, the actuality of rational numbers to be not embraced by the followers of Pythagoras. This resulted to Hippasus’ being drowned in ~ sea which was stated to it is in a penalty from the gods throughout that time.


What are Integers?

From the Latin native “integer”, which converts to “whole” or “untouched”, this numbers perform not have fractional or decimal components as with whole numbers. The numbers include positive natural numbers or the counting numbers and also their negatives. For instance, -3, -2, -1, 0, -1, 2, 3 are integers. The normal illustration room equally spaced numbers on an unlimited number line v zero, which is neither hopeful nor negative, in the middle. Hence, the positives are better than the negatives.

Regarding the history, the complying with accounts trace how integers were very first utilized:

In 200 B.C. Negative numbers were an initial represented through red rods in ancient China.In roughly 630 A.D., an unfavorable numbers were supplied to stand for debt in India.Arbermouth Holst, a German mathematician presented integers in 1563 as device in addition and multiplication. He developed the mechanism as a response to the increasing variety of rabbits and elephants which the was trying out on.

The complying with are the attributes of integers:


The number at the ideal side that the number line are positive and also they regularly represent the greater value the their negative counterparts.


The numbers at the left next of the number heat are often viewed together the lesser conventional value the their optimistic counterparts.


The center of the number line, zero is the integer i beg your pardon is neither confident or negative.

No fragments

Like entirety numbers, integers have actually no decimal points nor fractions.

Difference between Real Numbers and also Integers

Scope of actual Numbers and also Integers

Real numbers encompass integers, rational, irrational, natural, and whole numbers. ~ above the various other hand, integers’ scope is mainly concerned with whole numbers i m sorry are an unfavorable and positive. Hence, genuine numbers are an ext general.


Real number can include fractions such together rational and irrational numbers. However, fractions cannot be integers.

Least-Upper-Bound Property

Real numbers have actually least-upper-bound-property i beg your pardon is likewise known as “completeness”. This way that a linear set of genuine numbers have subsets with supremum qualities. Top top the contrary, integers execute not have actually the least-upper-bound property.

Archimedean Property

The Archimedean Property, i m sorry is the assumption that there is a natural number that is equal to or higher than any type of real number, can be used to actual numbers. Top top the contrary, the Archimedean building cannot be applied to integers.


Real numbers space a type of ar which is an important algebraic framework where arithmetic processes are defined. On the contrary, integers are not taken into consideration as a field.


As a set, actual numbers space uncountable when integers space countable.

Symbols of real Numbers and Integers

Real numbers are symbolized as “R” if a collection of integers is symbolized together “Z”. N. Bourbaki, a team of French mathematicians in the 1930s, stated “Z” native the German native “Zahlen” which way number or integers.

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Word origin for actual Numbers and Integers

Real numbers denoted the real roots the a polynomials while integer came from the Latin word, “whole” as they carry out not incorporate decimals nor fractions.

Real numbers vs Integers


Summary of actual Numbers vs. Integers

Both genuine numbers and also integers can be plotted on the number line.Integers is a subset of actual numbers.Integers have negative numbers.As a set, actual numbers has actually a much more general limit as compared to integers.Unlike integers, genuine numbers may incorporate fractions and decimal points.Properties of the least-bound, Archimedean, and field are normally applicable to real numbers yet not come integers.Unlike genuine numbers, integers room strictly countable.“R” stand for real numbers if “Z” is for integers.