Leaderboard

You’d have to find them all first.

Some infinite sets do, some do not. For instance the set of all values of the function f(x) = exp(-x) for all x >= 0 have a greatest element exactly = to 1 This particular infinite set has no least element. A different function, eg the sine function has both a greatest and a least element. Sorry, no.

With green burial, conversion into soil, plants, animals that eat those plants, fungi, worms, soil nematodes, and (if your mortician was lazy and irresponsible) residues of mercury from dental amalgam leaching into the soil. Make sure you find a reputable and environmentally aware mortician, if you want a green burial, so that your fillings will be properly removed.

That god darned catch-22 again... Kinda sums up the topic though. 😉

Frankie Howerd's best known catch-phrase was "Titter Ye Not !" - So the caption should probably have read "Twitter Ye Not !" 😉

I assume the objective must be to precipitate MgCO3. Mg(HCO3)2 does not exist as a solid (presume the Mg ++ cation is too small for 2 big HCO3- anions) so it won't precipitate as bicarbonate. Or alternatively just to convert dissolved CO2 to HCO3- in solution. But it seems at first glance a bit daft. Where would anyone get huge enough quantities of Mg(OH)2 from, in order to make an impact on the vast amount of CO2 dissolved in seawater? I've found the publicity blurb from the company in question: https://www.planetarytech.com/projects/cornwall/. It looks as if it is just a small scale exercise to confirm some models. There is no explanation of where they would get enough minerals to make a real change to the oceanic CO2 level, or what the effect might be of jacking up dissolved bicarbonate and metal cation concentrations. I do not believe it would be biologically neutral.

I am sorry you felt like that since nothing could be further from the truth. You are most definitely not an idiot since greater minds that yours or mine have been baffled by this question. I have noticed since that I mistakenly assumed your set S to be a set of number when in fact I see now that you stated clearly a set of sets. This brings us to the crux of greater minds since this is exactly the situation brought about by Russel's Paradox. That is when you try to apply Cantor - ZFC naive set theory to infinite sets that cannot be members of themselves. This is why Russell and Whitehead introduced the theory of types or classes, which is basically a reclassification of sets introducing a hierarchy of set types. This also paved the way for 'orders of logic' so ZFC is first order, infinite sets of sets is second order which is needed to correctly analyse infinite first order sets of numbers. In general you need a higher order of logic than the one you want to analyse and there are an unknown, perhaps indefinite or infinite, count of orders. This situation lead, in turn, to Godel's famous theorems about the subject. The best plain explanation of all this I have come across is put forwards in Hofstadter's award winning book Godel Escher Back

I wouldn't say in this case, "as n goes to infinity", because n doesn't "go" at all here, but rather is one arbitrary member of the set / sequence. Also, the expression, "for all n element of N", doesn't make sense to me in this case. One could write that there is mapping from the set N to set of rows such that every n in N is mapped to a row {1,2,3, ..., n}. See, e.g., Mapping | mathematics | Britannica.