Notation: Using $\prod A_i$ for noncommuting $A_i$

Question

I am writing up some math and realized that I do not know whether $\prod_{i=1}^m A_i=A_mA_{m-1}\cdots A_1$, OR whether $\prod_{i=1}^m A_i=A_1A_2\cdots A_m$.

Is there accepted consensus on this ordering?

Answer 1

Exactly as is mentioned in the comments, the more common notation is probably $$\prod_{i=1}^mA_i=A_1A_2\dotsm A_m,$$ but to be unambiguous, it is definitely good practice to first define your notation before using it. That is, add a line like

We write $\prod_{i=1}^m A_i$ as shorthand notation for the product $A_1A_2\dotsm A_m$.