![]() ![]() The word “Integer” Integer has its roots in the 16th-century Latin word “integer”, meaning “whole” or “intact”. In 1563, Arbermouth Holst invented the Integer number system to help him with an experiment involving bunnies and elephants. All whole numbers (integers) are rational numbers, and can be expressed as a fraction simply by using a denominator of 1. They were called “real” only because they were not “imaginary”. (examples: -7, 2/3, 3.75) Irrational numbers are numbers that cannot be expressed as a fraction or ratio of two integers. ![]() Origins René Descartes coined the term “real” in the 17th century to describe the roots of a polynomial which were not imaginary. Rational numbers are numbers that can be expressed as a fraction or part of a whole number. The set of all Integers is represented by “Z”. Hence, every natural number is a rational number but a rational number need not be a natural number. are rational numbers but they are not natural numbers. ![]() Notational symbol The set of all Real Numbers is represented by “R” or “ℝ”. Thus, every natural number is a rational number. Countability Real numbers form an uncountable infinite set. Whole numbers and their negatives on the number line are integers. Representation on the Number Line Any point on the number line is an actual number. An integer cannot be a fractional or a decimal number. Fractional numbers or decimals are real numbers. Only whole numbers and their negatives are classified as Integers. We can represent the rational number on a number line by. Technically, a binary computer can only represent a subset of the rational numbers. Every integer is a rational number and, but not all rational numbers are integers. The classic examples of an irrational number are 2 and. In case, the decimals seem to be never-ending or non-recurring, then these are called irrational numbers. If the decimal form of the number is terminating or recurring as in the case of 5.6 or 2.141414, we know that they are rational numbers. Likewise, an irrational number cannot be defined that way. All integers, whole numbers, natural numbers, and fractions with integers are rational numbers. Comparison Table Parameter of Comparison Real Numbers Integers Classification Integers, rational, irrational, natural, and whole numbers are all classified as Real numbers. A rational number is defined as a fraction (a / b ), where a and b are both integers and ( b < > 0).![]()
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