TITLE: Vertical bar sign in Discrete mathematics
QUESTION [24 upvotes]: I am little bit confused about the sign " | ".  Some people call it the division sign and some call it "such that".  In computer programming, it's known as pipe. 
| => Such that sign
| => Division sign
| => Pipe sign

REPLY [18 votes]: In number theory the sign $\mid$ denotes divisibility.  But you need to carefully note that this is definitely not the same as division.

"$2$ divided by $6$" can be written $2/6$ or $2\div6$.  Its value is one third, or $0.333\ldots\,$.
"$2$ divides $6$" can be written $2\mid6$.  This is a statement and does not have any numerical value.  It says that $2$ goes into $6$ exactly with no remainder, or that $6$ is an integer times $2$.  This statement is true.
Likewise, $3\mid7$ is the statement that $3$ goes into $7$ exactly with no remainder.  This statement is false.

It is very important to note (especially if English is not your first language) that "$a$ divides $b$" is very different from "$a$ divided by $b$".  Other ways of saying "$a$ divides $b$" are "$a$ is a factor of $b$" and "$b$ is a multiple of $a$".
Hope this helps!