(Not a duplicate of If "multiples" is to "product", "_____" is to "sum")
When working with sums or series, I often refer to $a_n$ in the summation $\sum\limits_n a_n$ as the "summand". Is there an analogous word for $b_n$ in the product $\prod\limits_n b_n$?
Wikipedia's description of "summation" makes several mentions of $a_n$ as the "summand" or "addend", but no equivalent is provided in the article on "product". My guess would be "multiplicand", but there appears to be a consistent definition (1, 2, 3) for it as referring to a specific number in a product. To paraphrase,
In the product $a\times b$, we call $b$ the "multiplicand" and $a$ the "multiplier".
I've also found that
- in the sum $a+b$, "summand" could refer to either $a$ or $b$; "addend" can be used interchangeably with "summand"
- in the difference $a-b$, $a$ is the "minuend" and $b$ is the "subtrahend"
- in the quotient $\frac ab$, $a$ is the "dividend" and $b$ is the "divisor"
- if $\star$ is an arbitrary binary operator, "operand" works like "summand" and can refer to either $a$ or $b$ in the expression $a\star b$
as summarized in this table.
"Summand" and "addend" being treated as synonymous almost mirrors the commutativity of $+$, but I suspect this is not the reason for their interchangeability. Optional: Is there a historical/etymological reason for making the distinction between the "multiplicand" $a$ and "multiplier" $b$ in $a\times b$, as well as the other operations listed above?
(The latter question may be more appropriate for the math history or English/Latin language SE's)