define:- real numbers, natural numbers, whole numbers, prime numbers, twin prime numbers...............
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A number is a mathematical object used to count, measure, and label. The original examples are the natural numbers 1, 2, 3, 4, and so forth.[1] Numbers can be represented in language with number words. More universally, individual numbers can be represented by symbols, called numerals; for example, "5" is a numeral that represents the number five. As only a relatively small number of symbols can be memorized, basic numerals are commonly organized in a numeral system, which is an organized way to represent any number. The most common numeral system is the Hindu–Arabic numeral system, which allows for the representation of any number using a combination of ten fundamental numeric symbols, called digits.[2][3] In addition to their use in counting and measuring, numerals are often used for labels (as with telephone numbers), for ordering (as with serial numbers), and for codes (as with ISBNs). In common usage, a numeral is not clearly distinguished from the number that it represents.
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real number:In mathematics, a real number is a value of a continuous quantity that can represent a distance along a line. The adjective real in this context was introduced in the 17th century by René Descartes, who distinguished between real and imaginary roots of polynomials.
Natural number:are a part of the number system which includes all the positive integers from 1 till infinity and are also used for counting purpose. It does not include zero (0). In fact, 1,2,3,4,5,6,7,8,9…., are also called counting numbers.
Natural numbers are part of real numbers, that include only the positive integers i.e. 1, 2, 3, 4,5,6, ………. excluding zero, fractions, decimals and negative numbers.
Note: Natural numbers do not include negative numbers or zero.
In this article, you will learn more about natural numbers with respect to their definition, comparison with whole numbers, representation in the number line, properties, etc.
whole number:The whole numbers are the numbers without fractions and it is a collection of positive integers and zero. It is represented by the symbol “W” and the set of numbers are {0, 1, 2, 3, 4, 5, 6, 7, 8, 9,……………}. Zero as a whole represents nothing or a null value.
Whole Numbers: W = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10……}
Natural Numbers: N = {1, 2, 3, 4, 5, 6, 7, 8, 9,…}
Integers: Z = {….-9, -8, -7, -6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9,…}
Counting Numbers: {1, 2, 3, 4, 5, 6, 7,….}
These numbers are positive integers including zero and do not include fractional or decimal parts (3/4, 2.2 and 5.3 are not whole numbers). Addition, Subtraction, Multiplication and Division operations are possible on whole numbers.
prime number: A prime number is a natural number greater than 1 that is not a product of two smaller natural numbers. A natural number greater than 1 that is not prime is called a composite number. For example, 5 is prime because the only ways of writing it as a product, 1 × 5 or 5 × 1, involve 5 itself.
twin prime number:A twin prime is a prime number that is either 2 less or 2 more than another prime number—for example, either member of the twin prime pair (41, 43). In other words, a twin prime is a prime that has a prime gap of two. ... However, it is unknown whether there are infinitely many twin primes or there is a largest pair.