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Quote from: Bored chemist on 13/10/2021 19:08:11Quote from: BilboGrabbins on 12/10/2021 16:44:56No you can't. Unless of course the room is infinite? But then how'd you know it's a room with walls?Yes, I can.I can align the table North/ South.And there are an infinite number of angles through which I can then rotate it.So that's an infinite number of "ways in which I can place a coffee table in a room."Lol. Are you being serious? A room has a finite boundary condition. You might get a hell of a lot of orientations but certainly not infinite. I don't like people misleading others into such baloney!

Quote from: BilboGrabbins on 12/10/2021 16:44:56No you can't. Unless of course the room is infinite? But then how'd you know it's a room with walls?Yes, I can.I can align the table North/ South.And there are an infinite number of angles through which I can then rotate it.So that's an infinite number of "ways in which I can place a coffee table in a room."

No you can't. Unless of course the room is infinite? But then how'd you know it's a room with walls?

I'm aware of this thought experiment... And no. You cannot divide infinitely. There is a physical stop sign in physics .

Quote from: BilboGrabbins on 13/10/2021 20:46:43Quote from: Bored chemist on 13/10/2021 19:08:11Quote from: BilboGrabbins on 12/10/2021 16:44:56No you can't. Unless of course the room is infinite? But then how'd you know it's a room with walls?Yes, I can.I can align the table North/ South.And there are an infinite number of angles through which I can then rotate it.So that's an infinite number of "ways in which I can place a coffee table in a room."Lol. Are you being serious? A room has a finite boundary condition. You might get a hell of a lot of orientations but certainly not infinite. I don't like people misleading others into such baloney!What boundary conditions stop me choosing an arbitrary angle?How many angles are there in the series 180, 90, 45, 22.5 ... and so on?Which of them is forbidden?

Hi again.Quote from: BilboGrabbins on 13/10/2021 18:40:57I'm aware of this thought experiment... And no. You cannot divide infinitely. There is a physical stop sign in physics . What physical stop sign in physics? Are you talking about an indivisible planck length? This was mentioned in reply #53. Otherwise lengths such as those in the tortoise and hare experiment or angles such as in Bored Chemist's example can be divided more times than any finite number of times (which is fair description of infintely many times) and it can often all be done within a finite amount of time.Best Wishes.

Yes the Planck length. This is the ground rule that prevents continuous divisibility.

Hi.Quote from: BilboGrabbins on 13/10/2021 22:27:22Yes the Planck length. This is the ground rule that prevents continuous divisibility. It's not a rule, it's one possibility. To the best of my knowledge we don't know that space is discrete rather than being continuous.Best Wishes.

It is a rule of physical length. No physicist doubts its existence. Well none I have spoken to.

Hi again. It's fine for you to have your opinions. I have my opinions and in fact I'm in the middle ground: Space might be discrete or it might be continuous.However, you need to be careful when you say something like this:Quote from: BilboGrabbins on 13/10/2021 22:48:21It is a rule of physical length. No physicist doubts its existence. Well none I have spoken to. It's not a universally accepted idea and you would need to cite some references.Here's one reference that counters what you've said and there are many others...... space and time can be either continuous or discrete in a quantum Universe. But it means that if the Universe does have a fundamental length scale, that the CPT theorem, Lorentz invariance, and the principle of relativity must all be wrong. It could be so, but without the evidence to back it up, the idea of a fundamental length scale will remain speculative at best..... [Taken from "This is why space needs to be continuous", Forbes. https://www.forbes.com/sites/startswithabang/2020/04/17/this-is-why-space-needs-to-be-continuous-not-discrete/?sh=50c668d774ea ]Best Wishes.

You've all been indoctrinated into accepting that you cannot divide by zero. Find out about the beautiful mathematics that results when you do it anyway in calculus. Featuring some of the most notorious "forbidden" expressions like 0/0 and 1^∞ as well as Apple's Siri and Sir Isaac Newton.In his book “Yearning for the impossible” one my favourite authors John Stillwell says “…mathematics is a story of close encounters with the impossible and all its great discoveries are close encounters with the impossible.” What we talk about in this video and quite a few other Mathologer videos are great examples of these sort of close encounters.

If we choose a simple room, which is the exact length of the table and one table stacked on the other defines the height, then how many orientations of a table can you make in this limited space?

Quote from: BilboGrabbins on 13/10/2021 22:22:49If we choose a simple room, which is the exact length of the table and one table stacked on the other defines the height, then how many orientations of a table can you make in this limited space?No, lets not pick a stupid example, carefully chosen so that you seem to be right.

Indeterminate: the hidden power of 0 divided by 0 ......... (and video provided)...

In today's video the Mathologer sets out to give an introduction to the notoriously hard topic of transcendental numbers that is both in depth and accessible to anybody with a bit of common sense. Find out how Georg Cantor's infinities can be used in a very simple and off the beaten track way to pinpoint a transcendental number and to show that it is really transcendental. Also find out why there are a lot more transcendental numbers than numbers that we usually think of as numbers, and this despite the fact that it is super tough to show the transcendence of any number of interest such as pi or e. Also featuring an animated introduction to countable and uncountable infinities, Joseph Liouville's ocean of zeros constant, and much more.

Hi again.I've got to ask: Do you know this Mathlogger person? Why are you promoting these videos? They're good - but what is this for? It takes time to watch these and you don't seem to want to discuss anything about them.Best Wishes.

They give us insight on how professional mathematicians are thinking about the problem.

...Or what they think is the best way to teach the problems to non-mathematicians.

I have posted my criticism on Cantor's diagonal argument which is used in the videos.

I think that diagonal argument produces more problems and inconsistencies, rather than being useful to solve other problems. So, getting rid of it could help mathematics to move forward and restore its consistency.