If the denominator happens to be unity, b = 1, the ratio is an integer. The numerator, "a", may be any whole number, and the denominator, "b", may be any positive whole number greater than zero. Rational Numbers - any number that is either an integer "a" or is expressible as the ratio of two integers, a/b.
Whole Numbers - the natural numbers plus the zero. The natural numbers are often referred to as the counting numbers and the positive integers. 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. Numerals - the symbols used to denote the natural numbers. The set of all integers is usually denoted by Z or Z+ĭigits - 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. The positive integers, 1, 2, 3., are called the natural numbers or counting numbers. Integers - Any of the positive and negative whole numbers. Some basic definitions of terms normally encountered in the classroom are given first. I also hope that after reading, digesting, and understanding the material offered herein, that you will have enjoyed the experience and that you will never utter those terrible, unforgettable words, "I hate math." It is sincerely hoped that the material contained herein will stimulate you to read and explore further. A list of excellent reading references is provided for those who wish to learn more about any specific number type or explore others not included.
The number type descriptions that follow will not be exhaustive in detail as space is limited and some would take volumes to cover in detail. In the interest of stimulating a broader interest in number theory and recreational mathematics, this collection will endeavor to present basic definitions and brief descriptions for several of the number types so often encountered in the broad field of recreational mathematics. Many, if not all, are marvelously unique and serve to illustrate the extreme natural beauty and wonder of our numbers as used in both classical and recreational mathematics. Over time, many of the infinite arrays, or patterns, of numbers derivable from the basic ten digits have been categorized or classified into a variety of number types according to some purpose that they serve, fundamental rule that they follow, or property that they possess. 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. In a sense, it could easily be concluded that we would not be able to live without them. Engineers, accountants, store clerks, manufacturers, cashiers, bankers, stock brokers, carpenters, mathematicians, scientists, and so on, could not survive without them.
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. 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. Number Theory - Learn All About Integers Numerals Natural Numbers Whole Numbers Rational Numbers Fractional Numbers and more!