Definition:Divisor (Algebra)/Real Number

Definition
Let $\R$ be the set of real numbers.

Let $x, y \in \R$.

Then $x$ divides $y$ is defined as:
 * $x \mathop \backslash y \iff \exists t \in \Z: y = t \times x$

where $\Z$ is the set of integers.

Also denoted as
The conventional notation for this is "$x \mid y$", but there is a growing trend to follow the notation above, as espoused by Knuth etc.

If $x \mathop \backslash y$, then:
 * $x$ is a divisor of $y$
 * $y$ is a multiple of $x$
 * $y$ is divisible by $x$.

In the field of geometry, in particular:
 * $x$ measures $y$

To indicate that $x$ does not divide $y$, we write $x \nmid y$.

Also known as
A divisor is also known as a factor.