# 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

Sad = happy x heart

If it suits, the usage of letters is due to their ease of writing. This comes from the intense repitition of them through the years. So which letter you pick does not matter, why n? The author felt like it?

• alright, but as I understand from @Newb, it's common to use n and m, and x and y in different specific cases? – Erik van de Ven Sep 23 '16 at 10:21
• 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
• Alright, thanks for all your responses. I've noted your explanation so I can look back at it later, if needed. Thanks again. – Erik van de Ven Sep 23 '16 at 10:26
• You're welcome, come back any time. If you feel my answer was of help consider accepting it :) – Zelos Malum Sep 23 '16 at 10:27

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.