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Number Set

Concept

Number Set

Listed below are some of the most significant number sets.

  • Natural Numbers, also called counting numbers, are the numbers used for counting. The set of natural numbers is denoted by N.\mathbb{N}.
  • Whole Numbers are the natural numbers in addition to zero. The set of whole numbers is denoted by W.\mathbb{W}.
  • Integer Numbers are the whole numbers in addition to their opposite. The set of integer numbers is denoted by Z.\mathbb{Z}.
  • Rational Numbers are the numbers that can be expressed as the ratio between two integers. The set of rational numbers is denoted by Q.\mathbb{Q}.
  • Real Numbers are the rational numbers, in addition to the numbers that cannot be expressed as the ratio between two integers. The set of real numbers is denoted by R.\mathbb{R}.
  • Complex Numbers are the numbers that can be written in the form z=a+bi,z=a+bi, where aa and bb are real numbers, and ii is the imaginary unit. The real part of a complex number is a,a, and the imaginary part is b.b. The set of complex numbers is denoted by C.\mathbb{C}.

Note that there are other significant number sets not shown in the Venn Diagram above, including:

  • Imaginary Numbers are numbers that can be written in the form a+bi,a+bi, where aa is any real number, bb is a non-zero real number, and ii is the imaginary unit. This set is represented with the symbol I.\mathbb{I}.
  • Irrational Numbers are the real numbers that cannot be expressed as the ratio between two integers. The set of irrational numbers can be written as RQ.\mathbb{R}\setminus \mathbb{Q}.
  • Prime Numbers are the natural numbers that have exactly two factors: 11 and themselves.