What does the "or" symbol mean as in "$ d\mid a$"

Question

What does the "or" symbol mean as in the following post:

How to prove $\gcd(a,\gcd(b, c)) = \gcd(\gcd(a, b), c)$?

In particular, the symbol is used in the above linked post in the following definition of $\gcd(a, b)$:

Given integers $a$ and $b$, there is one and only one number $d$ with the following properties.

$d \geq 0$

$d\mid a$ and $d\mid b$

$e\mid a$ and $e\mid b$ implies $e\mid d$.

It is not an "or" symbol, it is a vertical bar. Saying it is an "or" symbol is already applying a (here inappropriate) interpretation to it. — Marc van Leeuwen, Dec 10 '14 at 11:08

score 2 · Answer 1 · answered Dec 10 '14 at 11:00

2

you mean $d|a$. It is not 'or' symbol. It means d divides a.

answered Dec 10 '14 at 11:00

Bhaskar Vashishth

11,279

did you mean divides absoulutely with remainder 0. – Talespin_Kit Dec 10 '14 at 11:01
@Talespin_Kit Yes, that's the meaning of "divides" here. – Jean-Claude Arbaut Dec 10 '14 at 11:03
@Jean-ClaudeArbaut could you please post the link to the citiation if you knew one. This is the first time i come a symbol which has this type of meaning. – Talespin_Kit Dec 10 '14 at 11:07
@Talespin_Kit https://en.wikipedia.org/wiki/Divisor – Jean-Claude Arbaut Dec 10 '14 at 11:09

Jean-Claude Arbaut · Accepted Answer · 2014-12-10T11:09:45.887

1

In this context, you write $a|b$ to mean that $a$ divides $b$, or equivalently, that there is an integer $m$ such that $b=ma$.

See the article Divisor on Wikipedia, and also Vertical bar for other uses of this symbol.

edited Dec 10 '14 at 11:09

answered Dec 10 '14 at 11:00

Jean-Claude Arbaut

23,277

What does the "or" symbol mean as in "$ d\mid a$"

2 Answers2