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Why should base 10 be special? I did this in binary, and the last digit repeats as 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1 What does that prove?

The clock stuff is what really marks this as numerology for me. Numbers like 360 degrees for a circle, are essentially an accident of history. (I don't mean they were randomly selected.) To later retrofit other math to those numbers, imagining they are special, is upside down. Then there's stuff like multiplying by ten "for base 10". What? The number was already in base 10; this is just fiddling. And what's special about base 10 anyway?

Please read my post again. It answers your question. (Your question does not make sense. Purposeful evolution is not a thing, and you will not get an answer that assumes it is.)

You have evolution back to front, by missing the natural selection part. It's not at all about an organism knowing what would be useful, then developing it. It's (in a nutshell) about random mutation sometimes making something that turns out to be useful, which is kept by providing an advantage. And note that eyes and ears don't spring into the current form in one go. e.g. https://en.wikipedia.org/wiki/Evolution_of_the_eye

From Mordred: "When one particle changes state it does not cause the other to change state. You can merely make predictions of state of the other particle by measuring the state of one of the pairs." Say you have two marbles and you know one is Blue and one is Red. You randomly get one and without looking at it - chuck it in that black hole, or send it far away in a rocket. Later you look at the marble you still have. If it's Red you instantly know the one in the black hole, or far away, is Blue. You didn't instantly make the other marble Blue.

I'm astounded cpu68 still thinks there's anything to this. https://www.thenakedscientists.com/forum/index.php?topic=86231.0

F=ma The force is felt while accelerating the item. If they move at a constant speed they can be touching but feel no reaction force. (Imagine two cars moving in line at 100 kph. They could be 10 metres apart. They feel no reaction force. The second car could be "touching" the first, and they'd still feel no reaction force. But if the second car is being used to speed up the first car, or the first is being used to slow down the second, then they feel reaction force. * ignoring lots of friction and drag and stuff.)

What's the deal with "let it be known"? It sounds like some kind of (magic) incantation like the free men of the land use in "legal" contexts.

Anyone worried should just get a safety coffin: https://en.wikipedia.org/wiki/Safety_coffin

See the link from StringJunky: https://en.wikipedia.org/wiki/Cosmic_distance_ladder#Standard_candles

Wow, all one paragraph.

Your keyboard has one caps lock key.

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?