I just read a book’s section about general sums and products of cardinal numbers along with Koenig’s theorem. I made the following summary. The topic is not important to me but I wanna mention it in my notebook, so I try to dense it into natural language. Can you check if my summary gets the gist about it?
You can not only add/multiply cardinal numbers pair-wise or finitely often, just like you can generalize the operations of union or intersection of sets for arbitrary quantities (of sets). Especially it holds that if a < b (a,b are cardinal numbers) and if a gets added up with cardinal numbers smaller or equal to a as often as b gets multipled with cardinal numbers bigger or equal to b then the resulting product is bigger than the resulting sum (Koenig‘s theorem). It looks reasonable even at first glance because a product is designed as multiple addings, so that a product grows faster than a sum in general.