Talk:Product of Summations is Summation Over Cartesian Product of Products

Happy for it to be merged with Product of Summations. It is similar.

Peter Driscoll (talk) 03:46, 10 September 2017 (EDT)


 * I need to analyse it to see whether this approach can genuinely be considered a different proof from the existing one. If they are essentially the same, we may regrettably have to ditch this, as the effort to bring it to house style may be considerable. --prime mover (talk) 04:00, 10 September 2017 (EDT)


 * Note that the statements of the two are not identical. In Product of Summations, $B = \{1\cdots m\}$ does not depend on $a \in A$. So it is a proper generalisation and ought to be treated as such. &mdash; Lord_Farin (talk) 05:12, 10 September 2017 (EDT)

Product of Summations talks about standard summation re-ordering. The cartesian product version, although related has a single sum and a cartesian product to iterate over. This is useful in one particular derivation of the Eulers Product formula for the zeta function. It allows the construction of the set of positive natural numbers from the cartesian product of powers of primes.

The result is not rocket science. Just a simple proof to get started with. Learn the rules of the game here.

Peter Driscoll (talk) 10:19, 10 September 2017 (EDT)


 * I had a look at house style. It is going to take a while to get used to. As I understand your structure, the proof should have its own page but be referenced by Product of Summations, with the result listed there. Can you rename this page to, Product of Summations is Summation Over Cartesian Product of Products. If renaming is not supported, then I will create the new page and you can delete this one.


 * Your house style doesn't seem to give examples. Examples are incredibly usefull.


 * Peter Driscoll (talk) 21:02, 10 September 2017 (EDT)


 * You should have the ability to rename: hover over More and click on Move (top right). I believe standard auths should get you this.


 * For house style there's actually fairly copious notes, but the suggested technique is by example. But it's a good start to note that all "big" operators like Union, Summation, Product etc. need to be on a line with "\displaystyle" in them somewhere before the invocation of the command, and that brackets around them need to be prefaced with \left and \right as appropriate, with braces for ease of making sure of the correct scope. (You will immediately notice the vast improvement of readability and presentational aesthetics.) Also, check out the use of the eqn template, into which all (for a given value of "all") multi-row equations and logical arguments are to go. --prime mover (talk) 01:33, 11 September 2017 (EDT)


 * Oh yes, and note that the eqn template automatically places the \displaystyle into every $\LaTeX$ string, so you don't need to add them there. I notice that you have already started experimenting with this.


 * Also note the "\mathop" that goes before the operator in the limits of e.g. \sum and \prod -- it adds an extra space around the operator. This was a kludge we learned early on that was needed for MathJax, usually excellent but has occasional clumsiness like this. --prime mover (talk) 01:37, 11 September 2017 (EDT)