## The Quaternion Numbers

In this article, we define the set H of quaternion numbers as the set of all ordered sequences q = <*x,y,w,z*> where *x,y,w* and *z* are real numbers. The addition, difference and multiplication of the quaternion numbers are also defined. We define the real and imaginary parts of *q* and denote this by *x* = ℜ(*q*), *y* = ℑ1(*q*), *w* = ℑ2(*q*), *z* = ℑ3(*q*). We define the addition, difference, multiplication again and denote this operation by real and three imaginary parts. We define the conjugate of *q* denoted by *q*
^{*}' and the absolute value of *q* denoted by |q|. We also give some properties of quaternion numbers.