Is this an accurate way to represent n! using Π?

Question

I recently learned of the $\Pi$ symbol, and was wondering if the following is an accurate way to represent $n!$:

$\Pi_{i=0}^{n-1} n - i$

See my comments here: http://math.stackexchange.com/questions/477835/have-you-seen-this-formula-for-factorial/477858#477858 — Daniel Donnelly, Oct 07 '13 at 08:37

score 2 · Accepted Answer · answered Oct 07 '13 at 08:13

2

Yes, apart from the missing parentheses: make it $$\prod_{i=0}^{n-1}(n-i)\;,$$ and you’ll be fine. As $i$ runs from $0$ up through $n-1$, $n-i$ runs from $n$ down through $n-(n-1)=1$, which is exactly what you want.

answered Oct 07 '13 at 08:13

Brian M. Scott

631,399

Thanks, I hadn't realized I needed the parentheses. Also, nice notation, I'll take a note of how you did that. – Brian Gesiak Oct 07 '13 at 08:15
@modocache: You’re welcome! – Brian M. Scott Oct 07 '13 at 08:17
@modocache: the brackets are just to avoid ambiguity over the orrder of taking the product and doing the subtraction – Henry Oct 07 '13 at 09:39

Is this an accurate way to represent n! using Π?

1 Answers1