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In mathematics, common number sets refer to well-known and frequently used sets of numbers
In mathematics, common number sets refer to well-known and frequently used sets of numbers. These sets play an important role in various branches of mathematics, including algebra, calculus, and number theory. Here are some of the most commonly used number sets:
1. Natural Numbers (N): This set includes all positive whole numbers starting from 1 and going infinitely. Symbolically, it can be represented as N = {1, 2, 3, 4, …}.
2. Whole Numbers (W): The set of whole numbers includes all non-negative integers, including zero. Symbolically, it can be represented as W = {0, 1, 2, 3, …}.
3. Integers (Z): The set of integers comprises all positive and negative whole numbers, including zero. Symbolically, it can be represented as Z = {…, -3, -2, -1, 0, 1, 2, 3, …}.
4. Rational Numbers (Q): Rational numbers are numbers that can be expressed in the form of a fraction (ratio) where the numerator and denominator are integers. The set of rational numbers includes both terminating and repeating decimals as well. Symbolically, it can be represented as Q = {a/b | a, b ∈ Z and b ≠ 0}.
5. Real Numbers (R): The set of real numbers consists of all rational numbers and irrational numbers. Real numbers can be expressed as decimals, fractions, or even non-terminating and non-repeating decimals (like pi or square root of 2). Symbolically, it can be represented as R.
6. Complex Numbers (C): Complex numbers are numbers of the form a + bi, where a and b are real numbers, and i represents the imaginary unit (√(-1)). Complex numbers consist of a real part and an imaginary part. Symbolically, it can be represented as C.
These common number sets are foundational concepts in mathematics and are used extensively in various fields of study. Understanding these sets and their properties is important for solving mathematical problems and equations.
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