Genady

It is quite clear with the numbers, but not with the segments: - What is a segment? - What is a segment division? - What is same sense? - What is introduction infinity? If I knew these definitions, I might be able to figure out if it is or it is not possible to exhaust all divisions of a line segment. As of now, there is no relation between segment and real numbers. The latter are built on rational numbers and their converging sequences. I don't see anything like that in the former.

Yes. How to represent a hierarchical structure in a table so that it is efficient for SQL queries.

To find out if such a smallest real number exists, we need to use a definition of real numbers. There are several equivalent ones, so let's pick one. It can be formulated rigorously, but here is the idea. Assume we know what rational numbers are (fractions of integers, k/n.) We then define convergent sequences of rational numbers. Then, we discover that not all such sequences, in spite of being convergent, have limits which are themselves rational numbers. Then, we extend the set of numbers by including all such limits, and define this extended set, real numbers. Now we can answer the question: can any real number be divided by 2 to get a real number? Let's take a real number, Q. By definition, it is a limit of some convergent sequence of rational numbers, let's say, the sequence q1, q2, q3, ... Now let's take another sequence of rational numbers: q1/2, q2/2, q3/2, ... It can be shown to be a convergent sequence. Then, by definition, its limit is a real number. Thus, any real number can be divided by 2 to get a real number. Hence, there is no smallest real number.

I make better green salads with homemade dressing, better vegetable biryani, better hummus than restaurants make. They make better sushi, better veggie burgers, better seafood soup. None of us make real New York bagels

I don't think there are such concepts as "interval of points" and "interval ends at ..." in math. I have no idea what revolving, breaking, and reattaching segments have to do with numbers and interval lengths. The former are not mathematical concepts, AFAIK. @Boltzmannbrain, I start to suspect that the root of confusion is here: you are talking about an actual physical segment, while the "real number line" is a mathematical concept. The "real" in the latter does not refer to "line", i.e., it is not a "real line." It refers to "number", i.e., they are "real numbers."

Yes, I should've replaced it from the beginning for clarity.

Thank you. This also explains why I never heard of it.

OK, thank you. But, no, thank you.

Because you use this word the second time and I have never seen it otherwise, I have to ask. What does it mean?

Yes, and they recognize this because they tend to doubt and to question. It's two different things.

Has been done already: Fable vs. Fairy Tale – Difference Wiki

Because they

Then it is a fable rather than a fairytale.

I disagree. It is very similar to an attitude toward foods (see another thread, https://www.scienceforums.net/topic/128942-restaurant-food-split-from-heat-regulation-obesity/?do=findComment&comment=1232233). Some people tend to believe, e.g., maybe you. Some, OTOH, tend to doubt and to question, e.g., I. And everything in between.

^^^ maybe a consequence of ->

Not all. Some people are very reluctant to eat unfamiliar stuff, e.g., my mother. Some, OTOH, want to try a new thing when they see it, e.g., I. And everything in between. Fortunately, I grew up in the Northern West Asia, and then lived in the Middle East, NYC, and now in Caribbean, so my interest in food diversity has been satisfied. But I met people - visitors - who being in such places were happy to find McDonald's BTW, there is no McDonald's in Bonaire

LOL

Did you try a good light?

Just wanted to add that it is a well-known phenomenon in astrophysics, the "superluminal motion". Superluminal motion - Wikipedia

The phrase "the points end at 1.5" is wrong. The correct phrase is, "the interval end at 1.5". This does not contradict not containing the point 1.5. For example, you can say that your property ends by the river, but the river is not on your property. If you distinguish between the interval and the point, there is no contradiction. Yes, this is correct. The length is 0.5 in both cases.

Yes, he can see that. But that stuff is not very close to the EH. The minimal stable circular orbit for non-rotating BH is 3 times farther from the singularity than EH. Anything below that will fall in.

I'm guessing here, but I don't think it will happen. Assuming they all free fall from far-far away, he will not catch up with anything ahead of him. All that stuff will be redshifted to undetectability, and he will not see it.

We don't say this. We might say about the left interval that it ends at 1.5, but it does not contain the end point. It contains everything before 1.5, i.e., everything that is < 1.5, but not the point 1.5. I don't see anything not logical here. Can you point to any contradiction? I don't see any geometrical issue at all. The length of the interval stayed the same as before.

Hi there. Welcome!

BTW, if my numbers are correct, they show a curious relativistic "optical illusion": In 0.5 s, the observer "sees" the ship 0.75 light-seconds closer. It looks like the ship moves faster than light!