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Difference between revisions of "Real number"

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A '''real number''' is a number that falls on the real number line. It can have any value. Some examples of real numbers are:<math>1, 2, -23.25, 0, \frac{\pi}{\phi}</math>, and so on. Numbers that are not real are  <math>\ 3i</math>, <math>\ 3+2.5i</math>, <math>\ 3+2i+2j+k</math>, i.e. [[complex number]]s, and [[quaternion]]s.
 
A '''real number''' is a number that falls on the real number line. It can have any value. Some examples of real numbers are:<math>1, 2, -23.25, 0, \frac{\pi}{\phi}</math>, and so on. Numbers that are not real are  <math>\ 3i</math>, <math>\ 3+2.5i</math>, <math>\ 3+2i+2j+k</math>, i.e. [[complex number]]s, and [[quaternion]]s.
  
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The set of real numbers, denoted by <math>\mathbb{R}</math>, is a subset of [[complex number]]s(<math>\mathbb{C}</math>). Commonly used subsets of the real numbers are the [[rational number]]s (<math>\mathbb{Q}</math>), [[integer]]s (<math>\displaystyle\mathbb{Z}</math>), [[natural number]]s (<math>\mathbb{N}</math>) and [[irrational number]]s (sometimes, but not universally, denoted <math>\mathbb{J}</math>). In addition <math>\displaystyle\mathbb{Z}^{+}</math> means positive integers and <math>\displaystyle\mathbb{Z}^{-}</math> means negative integers. The real numbers can also be divided between the [[algebraic number]]s and [[transcendental number]]s, although these two classes  are best understood as subsets of the [[complex number]]s.
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The set of real numbers, denoted by <math>\mathbb{R}</math>, is a subset of [[complex number]]s(<math>\mathbb{C}</math>). Commonly used subsets of the real numbers are the [[rational number]]s (<math>\mathbb{Q}</math>), [[integer]]s (<math>\mathbb{Z}</math>), [[natural number]]s (<math>\mathbb{N}</math>) and [[irrational number]]s (sometimes, but not universally, denoted <math>\mathbb{J}</math>). In addition <math>\mathbb{Z}^{+}</math> means positive integers and <math>\mathbb{Z}^{-}</math> means negative integers. The real numbers can also be divided between the [[algebraic number]]s and [[transcendental number]]s, although these two classes  are best understood as subsets of the [[complex number]]s.
  
  
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*[[Irrational number]]
 
*[[Irrational number]]
 
*[[Complex number]]
 
*[[Complex number]]
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[[Category:Definition]]
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[[Category:Number theory]]

Revision as of 18:09, 25 November 2007

A real number is a number that falls on the real number line. It can have any value. Some examples of real numbers are:$1, 2, -23.25, 0, \frac{\pi}{\phi}$, and so on. Numbers that are not real are $\ 3i$, $\ 3+2.5i$, $\ 3+2i+2j+k$, i.e. complex numbers, and quaternions.

The set of real numbers, denoted by $\mathbb{R}$, is a subset of complex numbers($\mathbb{C}$). Commonly used subsets of the real numbers are the rational numbers ($\mathbb{Q}$), integers ($\mathbb{Z}$), natural numbers ($\mathbb{N}$) and irrational numbers (sometimes, but not universally, denoted $\mathbb{J}$). In addition $\mathbb{Z}^{+}$ means positive integers and $\mathbb{Z}^{-}$ means negative integers. The real numbers can also be divided between the algebraic numbers and transcendental numbers, although these two classes are best understood as subsets of the complex numbers.


See Also

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