# Why n and what does it mean?

Maybe a bit too early to ask, but I give it a shot. I'm trying to study mathematics again during my free time. Now I tried to figure out what exactly is meant with the multiple. Well this formula makes it quite easy to understand for me, but it's not totally clear yet:

a = n x b


So if I understand the formula correctly, for 15 = 3 * 5 15 is a multiple of 5, and for 15 = 5 * 3 15 is a multiple of 3, so 3 and 5 can both be a multiple of 15. But what I don't understand, why n? Why not just a = b x c? I cannot really find an answer for this either, in my study book they just start with formulas like:

an x a m = a n+m

without any further explanation why to use n or m. Hopefully somebody has an explanation for me

• What you call a variable doesn't matter. The underlying math is the same. However, there is some convention, like $n$ and $m$ are usually integers. $x,y$ are usually real numbers. – Newb Sep 23 '16 at 10:15
• haha woops, typo. But ok, so it doesn't really matter, but how n and m for integers, and x and y for real numbers. Thought they are the same, both rational numbers right? – Erik van de Ven Sep 23 '16 at 10:18
• Just found a nice explanation about the difference between real numbers and integers by the way: youtube.com/watch?v=gtiJTRd_DHM Didn't knew real numbers consists of integers as well as rational numbers and integers are, well, just integers. Now it's absolutely clear. – Erik van de Ven Sep 23 '16 at 15:11

Why not? Any letter or symbols work. You could have emoticons such that

• n and m are commonly used for integers and x and y is usually more just about everything. However in all contexts the type is made clear by for example saying $n,m\in\mathbb{Z}$ and so on, however one can use any letter for anything as long as the representation and source is made clear. In my work I have used n and m for well....everything and anything, wether it is integer or not just because of comfort on the keyboard. – Zelos Malum Sep 23 '16 at 10:23
• @ErikvandeVen There definitely are some more common conventions, e.g. $n$ and $m$ are often integers. But this is far from universal, so you always have to make sure what the variables are defined as in the text. – Eff Sep 23 '16 at 10:23
The author probably wanted to stress that he was talking about integer multiples of $b$. $n$ is commonly used to denote natural numbers. Of course, $a$ and $b$ are also naturals here, but the formula could also work with $a,b$ rational or real.
It is also pretty common to work with letters in the same alphabetic range to denote a similar role/type. For instance, a polynomial will have coefficients $a,b,c,d,\cdots$. For the same reason, $i,j,k,l,m,n$ often denote integers (indexes or counts). $x,y,z,t,u,v,w$ often denote unknowns or variables.