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Solution for what? I fail to see anything that needs a solution! (That's why I'm out for now. This is clearly going nowhere.)

Yes, there's no largest natural number, because there's infinite of them, yet no individual number is infinite. Infinity is weird like that. I'm out for now.

So what is the "largest" natural number in the set of natural numbers?

Sure, why not? Why is that an issue? Do you think we should stop at 3 billion metres?

Each metre of paint is a nice finite metre. But the line is an infinitely long line (made up of finite metres). I really don't see any issue deserving attention.

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?

That starts with "n∈N". So n is a member of the set of Natural numbers. That set is infinite. Any given selected value for n will be finite, and can be plugged into the "1≤x≤n" to make a finite list of 1 to n; but that n can be selected from any of the Naturals ... and there are infinite of them.

Just a few posts ago you wrote (my bold) "I forgot to put more ellipsis under the n for indefinite rows in the OP." This is what I tried to show with: 1 { 1 } 2 { 1, 2 } ... { 1, 2, ... } There is no single finite n in N that gives a set with no end. The list ( { 1, 2, ... } ) is infinite, and the row number is also infinite. Try thinking of the list ( { 1, 2, ... } ) as X on a graph and the list of lists as the Y. It's unbounded on both axis.

Cool. So maybe it's still all just a notation problem. Personally I think it's awkward to be using "n" when thinking of "infinite". Are you happy with the following? Does this have a "problem"? 1 { 1 } 2 { 1, 2 } n { 1, 2, ..., n } ... { 1, 2, ... } (I don't claim this is formal notation.)

By "the naturals" I took him to mean "the set of natural numbers", not "any given number in that set". (Edit: I've seen people in forums claim that "natural" numbers must have some limit, as they over-think what "natural" means and make claims like there can't be higher number than the count of atoms in the Universe (seriously, have seen stuff like that). So I did want to double-check that the OP did not have some kind of "N is finite" thinking.)

If n is infinite, then it doesn't end. That's not a "problem". Why would it be? nth row (where n is infinite) -> {1, 2, 3, ... } -> N Correct. (Edit: for your list of distinct Naturals) Not quite sure what you mean here. What?? Why do the naturals have to be finite? If that's not a typo, it may be the cause of your confusion.

Then you simply need to make your mind up on whether n is infinite or not. If it's not, then your list is finite and has an end: 8888 { 1, 2, 3, ..., 8887, 8888 } If it is, then your list is also infinite and has no end: ... { 1, 2, 3, ... } The only "issue" comes in limiting n to some finite number, then wondering why the list doesn't contain all of N. Plainly, if you limit n to 1,000, then 1,001 won't be in your list.

Boltzmannbrain, now knowing n in your OP is not meant to itself be infinity ("Note: I forgot to put another downward ellipsis under the n in the OP."), then its line would be: n {1, 2, 3, 4, ..., n-1, n } n is not infinity, the set does not have infinite numbers in it. If n = 1000, then there are 1000 numbers in the set. Happy so far? Now add 1 to n. And again, and again. Each time you add another number to the set. 1000 { 1, 2, 3, ..., 999, 1000 } 1001 { 1, 2, 3, ..., 1000, 1001 } 1002 { 1, 2, 3, ..., 1001, 1002 } When/why do you stop? Is there a last n?

Just because: https://en.wikipedia.org/wiki/The_Weapon_Shops_of_Isher

Yeah, but radians ... https://m.xkcd.com/2748/

Even Lego knows. This is very public knowledge. The initial ladder descent was filmed by a flip out camera. After that, well, there were two people in the lander. (Per the mod post, I don't mean this to become a topic, but this is a specific technical engineering detail you should know.)

No x 2. The indigenous people of New Zealand are the Maori. https://en.wikipedia.org/wiki/Māori The "O" in "OMC" is from "Otara". This is a low-income area of Auckland, our biggest city. https://en.wikipedia.org/wiki/OMC_(band)

How much energy would be involved in a "moon that fell"? What would be the effect on the materials involved? Can you show that the claimed moon would have remained a ball (while being embedded within the Earth)? ... yet somehow only that part on the surface then becomes part of our plate tectonics? Have you read-up on theories about out current moons formation?

What observer will agree with this?

Firstly, a car that's hydrogen powered isn't "burning" the hydrogen the way you may be thinking; a chemical reaction between the hydrogen and oxygen is used to make electricity to power motors. Yes, you could collect the water coming out of something hydrogen powered. But, it takes energy to separate the hydrogen from the oxygen. (That's where the hydrogen is going to come from in the first place; factories or whatever using electricity to separate hydrogen and oxygen.) (And, you'd have to carry that water around.) You're not going to get a free ride.

(deleted, I'm just tired.)

Imagine trying again, with the front and back windows removed from the van. (As this was posted in the "relativity" section, kjp, is your next step to compare the fly with the photon of a light clock?)

If you are in an accelerating rocket ship, you will feel yourself pressed into your seat. It's hard to see how the rest of the Universe decelerating would cause you and your seat to press together. Acceleration is an absolute, in that if you are holding a coffee cup, you might spill some coffee. Sitting at my desk my coffee does not spill, whether I consider myself at rest and the spaceship flying past Earth (at constant speed) to be moving; or if the alien in the ship considers itself as at rest and Earth is flying past. An Earthquake, which moves me around (accelerating) will make me spill my coffee.

Most current T.V. remotes are based on consumer infrared. About 15 years ago I had wireless headphones that used infrared (what we use bluetooth for nowadays). So yes, signals can be modulated onto an infrared carrier. Way less flexible than bluetooth etc, not sure why it'd be a choice now for "radio". You'd need to be close to the transmitter and in good line of sight.

Sorry, that probably wasn't a differential lock. That was probably for free wheeling hubs. It disconnected (or connected) your front hubs to the front axles. It was so when you were driving along in 2 wheel drive, the front wheels could turn without turning the front diff or the front drive shaft. Saves fuel and wear and tear (including tyres). One of my Father's several Land Rovers (this one was a Series II soft top) had such manually controlled front hubs. If I was out with him, it was my job to hop out with a short bit of broom handle, with a slot cut in the end, to activate/deactivate the hubs. More modern vehicles do this automatically.