numbers

Types of Numbers

Compiled by William Tappe

Introduction

         Those ten simple symbols, digits, or numbers that we all learn early in life that influence our lives in far more ways than we could ever imagine. Have you ever wondered what our lives would be like without these 10 elegant digits and the infinite array of other numbers that they can create?

Birthdays, ages,height, weight, dimensions, addresses, telephone numbers, license plate numbers, credit card numbers, PIN numbers, bank account numbers, radio/TV station numbers, time, dates, years,directions, wake up times, sports scores, prices,accounting, sequences/series of numbers, magic squares, polygonal numbers, factors, squares, cubes, Fibonacci numbers, perfect, deficient, and abundant numbers, and the list goes on ad infinitum. Engineers, accountants, store clerks,manufacturers, cashiers, bankers, stock brokers, carpenters, mathematicians, scientists, and so on,could not survive without them.

 In a sense, it could easily be concluded that we would not be able to live without them. Surprisingly, there exists an almost immeasurable variety of hidden wonders surrounding or emanating from these familiar symbols that we use every day, the natural numbers.

Numbers - The Basics Integers - Any of the positive and negative whole numbers, ...,  - 3,  - 2,  - 1, 0,  + 1,  + 2,  + 3, ... The positive integers, 1, 2, 3..., are called the natural numbers or counting numbers. The set of all integers is usually denoted by Z or Z+

Digits - the 10 symbols 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9, used to create numbers in the base 10 decimal number system.

Numerals - the symbols used to denote the natural numbers. The Arabic numerals 0, 1, 2, 3, 4, 5, 6,7, 8, 9 are those used in the Hindu-Arabic number system to define numbers.

Natural Numbers - the set of numbers, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17,....., that we see and use every day. The natural numbers are often referred to as the counting numbers and the positive integers.

Whole Numbers - the natural numbers plus the zero.

Rational Numbers - any number that is either an integer "a" or is expressible as the ratio of two integers, a/b. The numerator, "a", may be any whole number, and the denominator, "b", may be any positive whole number greater than zero. If the denominator happens to be unity, b = 1, the ratio is an integer. If "b" is other than 1, a/b is a fraction.

Fractional Numbers - any number expressible by the quotient of two numbers as in a/b, "b" greater than 1, where "a" is called the numerator and "b" is called the denominator.

Irrational Numbers - any number that cannot be expressed by an integer or the ratio of two integers.Irrational numbers are expressible only as decimal fractions where the digits continue forever with not repeating pattern. Some examples of irrational numbers are .

Transcendental Numbers - any number that cannot be the root of a polynomial equation with rational coefficients. They are a subset of irrational numbers examples of which are Pi = 3.14159... and e =2.7182818..., the base of the natural logarithms.

ALPHAMETIC NUMBERS Alphametic numbers form cryptarithms where a set of numbers are assigned to letters that usually spell out some meaningful thought. The numbers can form an addition, subtraction, multiplication or division problem. One of the first cryptarithms came into being in 1924 in the form of an addition problem the words being intended to represent a student's letter from college to the parents. The puzzle read SEND + MORE = MONEY. The answer was 9567 += 1085 = 10,652. Of course, you have to use logic to derive the numbers represented by each letter..

AMICABLE NUMBERS Amicable numbers are pairs of numbers, each of which is the sum of the others aliquot divisors. For example, 220 and 284 are amicable numbers whereas all the aliquot divisors of 220, i.e., 110, 55, 44,22, 10, 5, 4, 2, 1 add up to 284 and all the aliquot divisors of 284, i.e., 142, 71, 4, 2, 1 add up to 220.Also true for any two amicable numbers, N1 and N2, is the fact that the sum of all the factors/divisors of both, Sf(N1 + N2) = N1 + N2.