Types of Numbers
october 2017 by neerajsinghvns
Types of Numbers
There are many different types of numbers,
Natural, or counting numbers . These are the first numbers you learn about as a child, perhaps as someone had you count the number of apples in a bag (1, 2, 3, 4, 6, ...). We will refer to this set of numbers as the positive integers.
Whole numbers . This is just the number zero included with the counting numbers (0, 1, 2, 3, 4, ...). We will call this the set of nonnegative integers.
Integers . These are the whole numbers, extended to include negative number values (...3, 2, 1, 0, 1, 2, 3, ...).
Rational numbers . Any number that can be expressed as a ratio of integers, or if you prefer a fraction. This includes all integers and numbers like 2/3, 12/5, 782387/2478923, 0/432, etc.. All rational numbers have a decimal equivalent. For example 11/4 = 2.75, 4/3 = 1.333333..., and 1/7 = 0.14285714285714285... The decimal equivalent of rational numbers always end in a repeating digit, or series of digits. The the three examples just listed, the decimal equivalent of 11/4 ends with a repeating 0, 4/3 ends with a repeating 3, and 1/7 ends with the sequence 14285 repeating forever.
Irrational numbers . Numbers that have a decimal equivalent, however they don't have a repeating digit or series of digits. This also means that one cannot find a ratio of integers that is exactly equal to the number. Common examples of irrational numbers are the square root of 2 and π.
Real numbers . All the rationals plus all the irrationals.
Imaginary numbers . Any real number multiplied by the square root of 1. Often the square root of 1 is referred to as i or j. So an imaginary number can be written as 3.2i or 8.77j. It is OK to use irrational multiplying numbers, so πj is a perfectly reasonable imaginary number.
Complex numbers . Any real number added to any imaginary number, such a 2+3j.
Types
of
Numbers

natural
whole
integers
rational
irrational
real
imaginary
complex
There are many different types of numbers,
Natural, or counting numbers . These are the first numbers you learn about as a child, perhaps as someone had you count the number of apples in a bag (1, 2, 3, 4, 6, ...). We will refer to this set of numbers as the positive integers.
Whole numbers . This is just the number zero included with the counting numbers (0, 1, 2, 3, 4, ...). We will call this the set of nonnegative integers.
Integers . These are the whole numbers, extended to include negative number values (...3, 2, 1, 0, 1, 2, 3, ...).
Rational numbers . Any number that can be expressed as a ratio of integers, or if you prefer a fraction. This includes all integers and numbers like 2/3, 12/5, 782387/2478923, 0/432, etc.. All rational numbers have a decimal equivalent. For example 11/4 = 2.75, 4/3 = 1.333333..., and 1/7 = 0.14285714285714285... The decimal equivalent of rational numbers always end in a repeating digit, or series of digits. The the three examples just listed, the decimal equivalent of 11/4 ends with a repeating 0, 4/3 ends with a repeating 3, and 1/7 ends with the sequence 14285 repeating forever.
Irrational numbers . Numbers that have a decimal equivalent, however they don't have a repeating digit or series of digits. This also means that one cannot find a ratio of integers that is exactly equal to the number. Common examples of irrational numbers are the square root of 2 and π.
Real numbers . All the rationals plus all the irrationals.
Imaginary numbers . Any real number multiplied by the square root of 1. Often the square root of 1 is referred to as i or j. So an imaginary number can be written as 3.2i or 8.77j. It is OK to use irrational multiplying numbers, so πj is a perfectly reasonable imaginary number.
Complex numbers . Any real number added to any imaginary number, such a 2+3j.
october 2017 by neerajsinghvns
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