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It's possible that the whole point of life is to facilitate the invention of potato chips. I don't think it is but it could be.

Life does not have a purpose. But people do, sometimes.

Tried it. Had trouble with the last bit. My sister had one. Tasted foul. And it feels sexier, like it's someone else's hand . . . . . So I'm told ! 😆

As I see your argument in plain English it is this:- Taking you list of sets from post#1 Set the indexing line counter aside for the moment as it is not really needed. Consider the set which contains every set on your list. If such a set exists, call it W . The listing of W then appears as in your list of sets without the indexing. IF you go on long enough why do you not arrive at the set {1,2,3,4...., (n-1), n (n++1)...}, why of course is N ? Of course N is also the indexing set we have ignored up to now. Note also that all the sets up to N are finite, but N itself is transfinite. I mentioned Russel's Paradox which queries the existence of W. This was one of the earliest expositions of many paradoxes that appeared around the 1890s to do with the size of sets. Hints of these difficulties go right back to the Ancient Greeks and Zeno in particular, although they did not have more modern set theory to place the questions in. A proper course of study into the whys and wherefores of these matters takes more than a year so most folks don't attempt it but look for a quick fix explanation. My offering to you is to consider the Greek approach, where they realised that there is more than one infinity. They distinguished two types of infinity viz potential and actual infinity. They believed that there are no instances of actual infinity, which we observe as for instance, the count of numbers between 1 and 2. But their potential infinity does not exist' either for a different reason. It does not exist because no finite process can ever get there. In other words the process does not terminate or goes on forever. Which is what I am suggesting is the reason why your list will never arrive at N. Cantor's approach considering magnitudes has run into difficulties why has yet to be fully resolved. There are at least three different mathematical/logical schemes to try to achieve this. After your year and more of study you would find that none are totally satisfactory as they all wrestle with the idea that some sets are just too big to be contained in other sets. Hopefully you can now sleep happy at night.

The difference is the way they get their energy input to work against entropy, basically. Desalination plants often use reverse osmosis, in which pressure is used to force water molecules through a semipermeable membrane that does not allow the larger, solvated, salt ions through. (Although an individual Na+ or Cl- ion is smaller than an H-O-H molecule, these ions in solution are surrounded by a solvent "cage" which is quite tightly bound to it and makes their effective size a lot bigger.) Alternatively distillation is used, often under reduced pressure to permit boiling at a relatively low temperature. (Boiling greatly increases the surface area for evaporation, accelerating the process, due to the surface area of the bubbles). The very large desalination plant at Jebel Ali, in the UAE, used that method, I remember, from when I lived in Dubai in the 1980s. It employed waste heat from the Jebel Ali steam power station - quite clever. A solar still relies on heat from the sun, rather than an artificial energy input. So the energy input is in a sense "free" - and non-polluting, of course - but you are limited to the energy density of sunlight. Solar stills also have to rely on evaporation at atmospheric pressure, which further constrains their capacity.

No fair asking for something that's impossible in the original problem 😠 "Proof": I think there might be a problem here talking about the area of points, like with the Banach-Tarski paradox.

Just some back of envelope stuff. Recast the objective as the transport of a nominal 100 tpd of deep ocean dissolved iron to the surface. Typical deep ocean iron concentration (from here) seems to be around 0.5 nM which sets the pumping volume to a little over 40,000,000 m3/s. While it is correct that the external water column does largely support the pumping effort, deep ocean seawater density is generally taken to be around 1050 kg/m3 as ooposed to the 1024 kg/m3 of surface waters and that 26 kg/m3 difference does give a static pressure difference of around 250,000 N/m2 per 1,000 m. If upward velocity were negligibly small (really huge diameter pipe) then a 100% efficient pump would consume a minumum VdP of 1TW / 1,000 m. As we're already exceeding the electrical power consumption of China and haven't yet touched on friction losses, I see little purpose in pursuing this further. Tankering in liquid fertiser is a far, far more cost effective method of meeting the initial objective. Whether or not the initial objective was a good idea, I'm with @Ken Fabian (as usual).

I'm doubtful that anyone who ever lived has achieved that goal.

Even easier is making cold brew. Get a cheese cloth, soak in water overnight. Tastes better. Wastes less. Can be stored in fridge just like you do now. https://twinsandcoffee.com/cold-bew-coffee-with-cheesecloth/ I have a machine that grinds while beans with each brew so I buy 3-lbs bags at Costco for $10 when they go on sale and it lasts forever. I save money by focusing my hypercaffeinated energy on to DIY projects that would cost thousands to have others perform.

People keep kicking them. They handle one more than the other. Looks like you had a vasectomy; one still has visible stitches ...

Interesting. I've seen similar while asking it to write from other perspectives or to write in the style of Shakespeare and other famous authors). Now... nobody tell it that it's better than Genghis and we should all be safe. @Genady May just be too much for it. @Sensei. I know lot of times it can be phenomenal. It's like a strange sort of idiot savant though not nearly so limited.

It is a very narrow view.

I think one difficulty would be that the salt would not drop back into the ocean. As each droplet progressively evaporated and shrank, the salt would become more and more concentrated, leading eventually to tiny particles of salt that would be carried inland by the breeze for long distances. I would propose instead to combine your idea with solar stills to generate fresh water for your pumps, returning brine to the ocean. In such hot deserts, one almost invariably gets a daily onshore breeze after about 11am, due to the rising of hot air over over the desert drawing in cooler air from above the sea. This normally persists until just before sunset. So it would be a fairly reliable process, I think. But I have no idea whether enough evaporation could be achieved to change the climate this way. I think I read some years ago that another way is simply to use the fresh water for irrigation and promote the growth of plants which, by their transpiration, start to alter the climate that way - and generate moisture-retentive soil, by the detritus on the ground that they create.