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Because I cannot say 'no' to my grandchildren.

When you say 'increase by 1' what exactly do you mean ? Are you counting or performing arithmetic ? These two processes are very different things, obeying different rules. In order to appreciate this here is a Wikipedia list of what you need to study, which demonstrates why I said it would take so long. I note you didn't reply to that post. List of statements independent of ZFC - Wikipedia It shouldn't be an issue once you realise this as things change once you include infinity. It is an axiom of (finite) arithmetic that there is a unique number Y which has the property that when added to any number , X, the result is x X + Y = X This unique number is of course more familiarly known as zero. However if you introduce infinity you also have X + ∞ = X Contradicting the axiom of 'additive identity' as this axiom is called. +1 to wtf and pzkpfw

I'm certainly lost as to what the issue is. Removing the sets from it all (as I think the basic issue is perhaps more fundamental and they just add noise): If we start writing "all" the natural numbers we start with 1, next is 2, then 3. All nice finite numbers. But there's no "last" natural number. We'll never write it down, even with infinite time, so we have notations, like maybe: 1, 2, 3, ... So "1" and "2" and "3" are easy finite numbers. But "..." represents "infinity", it's not a specific value, here it's "all the values". Yes, we go "finite, finite, finite, infinity" (using the terms from a post about a day ago), but how is this any kind of issue?

@zapatos Ten years ago+ I bought a video camera with selfie feature and found that it didn't have a built-in timelapse feature. So I started poking around how to send commands to the camera via USB (WiFi/BT unavailable) and wrote an application for the computer that sends these commands by wire and then automatically downloads the photo and deletes it from the camera's memory. A cool project in the C++ .NET Framework for a weekend with a beer (or ten).. These days people merge 4x 2TB NVMe drives (RAID-0) to have one continuous 8 TB drive (600 USD investment), to be able to edit lengthy videos in UHD resolution (3840x2160). The better input source resolution, the better final quality on-line.. If you're doing timelapse, the sound/voice is added post-factum, so you'll tell what you want to the people watching it. They would have had no idea of the error if you hadn't said so.

If nothing else this utility model has served as a lesson that gaining answers to these types of questions before doing the work of developing the 'invention' might lead to better results afterwards.

I put this up a few years back, over the “Time Service” sign at work. Not many people noticed. Had to wait a year from my original plan, owing to rain. (paper sign) I got rained out again and couldn’t do a “Navel Observatory” one last year.

It would be funnier, and self-paying, if you set up a couple of cameras around you on tripods while you work, and create a "how I did it" timelapse and then upload it to YouTube, Vimeo, TikTok, FB and IG..

I don't think so. Membrane doesn't affect flavor and will add a tiny bit of collagen (a good thing) to your coffee. On the road this week, so am slow to reply here. Many useful ideas, though I am not driving over walnuts for a week then working them over with a jackhammer and a sawzall or whatever the next steps were. Another money saver: make your rice go a little farther, and and add protein, with saved nail clippings.

Ha, yes I never really give that a thought, well done!

Intuition is that rotation will complicate things because it allows for more ways in which a shape can be moved to dodge the grid, but it seems not to matter because it can still be placed off the grid without rotation.

That’s awesome!

To get rid of the outer hull we throw them in the driveway and drive over them for a week or so. We've also put them into a cement mixer with rocks and water. Did a great job of getting rid of the hulls, plus made the inner hulls nice and clean. To get through the inner shell we use a wire cutter. At the pointy tip you clip between the two halves and the shell pretty much splits in half. Then you clip into the fat part of one of the halves and it drops into quarters which exposes the meat which can be pulled out. It's not quite that easy but it's pretty close. I find it really easy. Usually all I have to do is bring my wife an occasional cup of coffee as she's working. 😀

To the best of my understanding of this thread, the heart of your issue seems to be that you don't quite get the following idea: Each of the individual natural numbers 0, 1, 2, 3, 4, 5, ... is itself a finite quantity. And there are infinitely many of them. In other words there are infinitely many finite things. And for some reason you have trouble going back and forth between those two levels. The finitude of each of the natural numbers, and the endlessness, or infinitude, of the procession of all of them via the process of endlessly adding 1. There are infinitely many natural numbers, and each of them are finite. Likewise each R(n) = {1, 2, 3, ..., n} is a finite set; and there are infinitely many of the finite sets R(n), namely R(1), R(2), R(3), etc. Hope this is helpful.

R(n) does not change to infinite. R(n) and {R(n)} are different things. The former contains numbers in the range [1, n]. The latter contains sets R(n) for all n's. The former is finite, the latter is not.

An old West Country tip on how to improve the crop of walnuts from your tree. You gather together on a certain day, and ceremonially "beat the bark" of all of the walnut trees. It's supposed to dramatically increase the yield of walnuts. I believe it still goes on today. The old saying goes : " A woman, a dog, and a walnut tree, the more you beat them, the better they be." Of course, this bit of wisdom is rather dated now, as these days, beating dogs is considered cruel.

I have to say, one of the best aids I ever bought was a simple basic shopping trolley on wheels. You know the ones that you see grannies wheeling their shopping home in. I have a big version of that. The one I have will happily carry thirty or forty pounds of shopping, and it makes all the difference because with that I can walk to the shops, instead of choosing to drive. I like to walk when I can for exercise, but lugging forty pounds of shopping on my back is out of the question. So it gives me much needed exercise, and saves a piddly bit of diesel money.

And this is the point I made earlier. There is no 'point' in living. We are just one of the many possible configurations of matter in this universe.

That's a very positive way of living your life but its not really a purpose (unless you make it a personal one). It's more of a code of practice, or method, or goal. As far as I can see, and I mentioned this earlier in the thread, if there is a purpose then it seems that the one purpose is survival, self survival long enough to aid in continuation of your species - reproduction. Why this is so? Who knows, but it makes sense in that, else basically and very simplistically, there would be no point in living in the first place.

How it works is pretty simple, and once you understand how it works it's not frightening and it's not going to replace us. It's no smarter than an elevator that knows what floor to stop on based on what button you pushed. They take a huge body of text, everything they can get their hands on. In fact the sources of this data are interesting and of course represent choices made by the programmers. In other words ChatGpt is built by humans and encodes the biases of the humans who built it. Here's their own description of the data. https://www.stylefactoryproductions.com/blog/chatgpt-statistics So they start out basically with a lot of digitized books, and a lot of web pages and Reddit answers. Nothing that isn't already digitized, and skewed toward Reddit users. Ok. Then they apply incredibly sophisticated statistical analysis to make up rules on the fly such as "When you see this phrase, 86% of the time you see this other phrase." They take that basic idea to its most sophisticated level, where ChatGpt can even pass law exams and explain physics to people. That's impressive statistical pattern matching. But at heart it is just a big adding machine, crunching text it doesn't understand, and figuring out what strings of symbols are typically followed by what other strings of symbols. It has no meaning. The meaning is in the minds of we humans. That's the difference. It flips bits. We experience meaning. It does not "understand" anything. It doesn't know anything. It doesn't feel anything. It just reads in some data and calculates the correlations among the data. It's so mechanical that you could program a computer to do it. And that's literally what they do. It's not a human being. It's a smart elevator. The real danger is the foolish humans who think it's some kind of god. Humanity's next graven image. Something to worship, something to fear, something to exploit. That's all, no more and no less than any of humanity's other clever tricks like fire and the wheel and the printing press and the Internet and civilization itself. ChatGpt-like systems are profound but not existential. We'll be fine.

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

Exactly.

The reason that I prefer population measures first, is because the climate problem is an hypothesis, whereas the population problem is very much a fact. We are causing extinctions because of land and sea use at a criminal rate right now, whereas climate may or may not become a problem a long time in the future, nobody knows. People think they know, but they don't. They are only convinced. Nobody knows the future, but you can know the present, and extinctions are happening today, were happening yesterday, and because of that, we can be very sure that they will be happening tomorrow. As well as extinctions, it's the destruction of habitats that I would like to see stop. Clearing more forests (with all the CO2 that that entails) and marginal land is causing damage and extinctions that will probably never be noticed, but will never be reversed.

That should be your first clue. Usually, the more I look into anything, the less strange and complicated it seems. And that's how it should be. Don't you think?