Genady

Not allowed

There is a round table and an unlimited supply of round tokens. Two players place in turn one token at a time anywhere on the table without overlapping other tokens. The last player to place a token, wins. What is a winning strategy?

Yep, I needed algebra as well: +1

You are right that if we want to know what they see with their eyes, we need to use Doppler formula. And of course the result is consistent with Lorentz transform because it is the same SR. However, to explain what happens, as opposed to what is seen, is straightforward: In the inertial frame A, B's time is dilated 1.25 times. Thus, while B's clock has advanced by 2 years, A's clock has advanced by 2.5 years.

That's how I thought about it, too.

Yes. +1

There is no problem, because the cda does not say that a constructed sequence does not appear in any list, but in the given list. Cantor's diagonal argument - Wikipedia

The list is very long. The very first use of calculus was to calculate motion of bodies and geometric properties of curves and shapes, such as their lengths and areas.

Calculus is a part of mathematics. Any more meaningful explanation would require some mathematical education. Maybe you could point more specifically, what don't you understand or what do you want to know?

I don't know why you say and what you mean saying that "space expansion is the only interpretation of cosmological redshift." Thus, I don't know what you are asking to justify. This is up to moderators.

I am not justifying it. I am answering your question, "it is called space expansion and not spacetime expansion. Why?" As I've said above, if you wish to suggest a different interpretation, go ahead.

In the metric, the second term on the right is spatial interval. As you see, it depends on the scale factor, a(t), which can change with time. OTOH, the first term which is temporal interval, does not change.

If you want to suggest a different metric for the homogeneous and isotropic universe, go ahead. If you want to suggest a better model of the universe, go ahead. Anyway, there is only one metric, the spacetime metric. In the FLRW metric, the space rather than the metric of space is expanding.

In the second part of the first sentence that you've quoted in the OP. It applies to any redshift, the cosmological one included.

We use GR. It is both. This how the metric of homogeneous and isotropic universe works. See FLRW metric.

A string is wound evenly around a circular rod exactly four times. What is the length of the string if the length of the rod is 12 cm, and its circumference is 4 cm?

Yes, relativistic Doppler effect includes time dilation. As I know of a solution to the twin paradox that does not include relativistic Doppler effect, could you refer to a solution that does?

PS. The mention of "always" in the OP means, "while the train moves forward."

That's the only part I know of. +1

Stew of Everything:

When a train moves forward there is always a part of it that moves backward relative to the ground. What part is it?

Yes, with a little subtlety. In democratic societies there are often several versions of history, accepted by different groups.

Perhaps you know that it is very difficult to modify constitution. Unfortunately, people go with it.

Constitution is a law that applies today. Unlike the historical facts.