Notation: is it correct to state $3a=a3$?

Question

If $a$ is a real constant, do you regard $3a$ and $a3$ as equal or different?

Answer 1

With usual conventions $\ 3a = a + a + a = a3.\ $ However, the latter might prove confusing because of the widespread convention to write "coefficients" before "variables" in expressions having polynomial form. This is part of the algorithm that leads to the standard normal form for polynomials $\,c_0 + c_1 x + \cdots+ c_n x^n\,$ with coefficients on the left. Because polynomials are ubiquitous, so too is this convention (or normal-form).

Answer 2

Both are technically correct, but convention is to write $3a$, not $a3$. If you write $a3$, it could be mistaken for $a_3$ or $a^3$. Not following convention in mathematical writing is like using poor grammar in English.

Answer 3

It's just how everyone has agreed to write it(3a). If you want to write it like a3 then I would make it (a)(3) so people know we are multiplying things.

Answer 4

If $3$ and $a$ were both elements in a non-Abelian group, it would be possible that $3a \ne a3$. The convention helps to emphasize that you're working in a set with commutative multiplication.