This means that a linear set of real numbers have subsets with supremum qualities. Real numbers have least-upper-bound-property which is also known as “completeness”.

Real numbers can include fractions such as rational and irrational numbers. On the other hand, integers’ scope is mainly concerned with whole numbers which are negative and positive. Real numbers include integers, rational, irrational, natural, and whole numbers. Like whole numbers, integers have no decimal points nor fractions.ĭifference between Real Numbers and Integers Scope of Real Numbers and Integers The center of the number line, zero is the integer which is neither positive or negative.

The numbers at the left side of the number line are often viewed as the lesser standard value of their positive counterparts. The numbers at the right side of the number line are positive and they often represent the higher value of their negative counterparts. The following are the characteristics of integers: He developed the system as a response to the increasing number of rabbits and elephants which he was experimenting on. Arbermouth Holst, a German mathematician introduced integers in 1563 as system in addition and multiplication.In around 630 A.D., negative numbers were used to represent debt in India.negative numbers were first represented with red rods in ancient China. Regarding its history, the following accounts trace how integers were first utilized: Hence, the positives are greater than the negatives. The usual illustration are equally spaced numbers on an infinite number line with zero, which is neither positive nor negative, in the middle. The numbers include positive natural numbers or the counting numbers and their negatives. This resulted to Hippasus’ being drowned at sea which was said to be a punishment from the gods during that time.įrom the Latin word “integer”, which translates to “whole” or “untouched”, these numbers do not have fractional or decimal components just like whole numbers. Unfortunately, the actuality of rational numbers was not accepted by the followers of Pythagoras. For instance, the square root of two, which is 1.41 cannot be expressed as a fraction hence, it is irrational. Through geometry, he proved that some numbers were irrational. Pythagoras’ student, Hippasus disagreed that all numbers were rational. For instance, 3/5 is a rational number but 3/0 is not. Where p and q are both integers and q is not equivalent to zero, p/q is a rational number. Rational numbers are the quotients or the fractions of two integers. Regarding its origins, Pythagoras, the ancient Greek mathematician proclaimed that all numbers were rational. Integers are whole numbers which include the negative side of the number line.Īlso known as counting numbers, natural numbers are like whole numbers but zero is not included as nothing can be essentially counted as “0”. Whole numbers are positive numbers which have no fractional parts nor decimal points as they represent whole objects without fragments or pieces. Real numbers include whole, integers, natural, rational, and irrational numbers: He particularly set the difference between Polynomials’ real roots and their imaginary roots. The description “real” was presented by Rene Descartes, a famous mathematician and philosopher in the 17th century. Those that fall on the right side are labeled as positive while those on the left are negative. Real numbers are the values you can find on the number line which is usually expressed as a geometric horizontal line where a chosen point functions as the “origin”. Hence, the key difference is that real numbers is a general classification while integers is a subset which is characterized as whole numbers which can have negative properties. Since real numbers include all rational numbers like the integers, they share similar characteristics such as the utilization of whole numbers and being plotted on the number line. Just like other concepts, number categories overlap. Mathematicians have developed systems to specify how a certain number is different from another.

Integers are rational numbers