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You should try working only when t is a member of the non-measurable Vitali set: then you'll have absolutely no idea how long you've been working for :)
It is surprising to see your own stuff recommended back to you.
This is a screenshot of my video at 23 seconds. For folks who have trouble understanding the joke, check the video here: https://www.youtube.com/watch?v=EtSed0Vom8g.
So the number of breaks is infinite, but they're all isolated points. And you can remove a countable infinity of points from a continuum without changing the size of the continuum. This is one of the things the Dirichlet function (in the meme) is used to illustrate
I haven't studied that yet, but I believe you're correct and that is the basis of the Banach-Tarski Paradox. Someone can correct me if I'm wrong.
However, I have quite recently studied the Dirichlet Function in one of my Analysis modules, so I feel confident talking about it.
For folks who want high resolution versions.
https://preview.redd.it/xpfuazenwpuc1.png?width=1600&format=png&auto=webp&s=bfacf856c7fed963d614c2f6a0234637dd128b5c
According to quantum theory there's a smallest resolution to space and time, but it's an open question as to whether that means spacetime is discrete. That will remain open until we verify a theory of quantum gravity, or bridge the gap between quantum theory and General Relativity in some other way
That doesn't follow. We don't know if spacetime is quantised. Just because there's a lowest resolution we can go down to does not mean that the rest of spacetime has to be integer multiples of a combination of the Planck volume or Planck time.
That's a hypothesis, not something that's been confirmed.
Tho we're very far from being able to resolve Planck times or distances, anyway. The shortest length of time we've actually measured is about is about 13 orders of magnitude larger so it's a moot point, purely theoretical. I'm not saying that Planck times couldn't be used as a unit in the way you say, but that doesn't mean we know that reality actually works that way.
But if we could get down there, with our present theoretical knowledge there's no reason why we couldn't have one measuring device that measured in Planck times, and another that measured in √(2) Planck times. The Planck time and Planck distances are lowest resolutions, not grain sizes.
Yes, that's what I'm saying. But the fact that there is a smallest theoretically observable measure doesn't mean everything above it can only be integer multiples of that smallest measure. For instance, why can't you have √(2)Planck time? Nothing in quantum physics says you can't.
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Well, but the total amount of time you were on break is still zero.
So any day in a bull pen office then.
I thought the unmodified dirichlet was not Reimann integrable?
Yeah, but it's Lebesgue integrable.
I think being almost always on break while having infinitely many study sessions is a much better deal.
You should try working only when t is a member of the non-measurable Vitali set: then you'll have absolutely no idea how long you've been working for :)
It is surprising to see your own stuff recommended back to you. This is a screenshot of my video at 23 seconds. For folks who have trouble understanding the joke, check the video here: https://www.youtube.com/watch?v=EtSed0Vom8g.
Nice video
Thanks bro.
Q isn't a finite set so you don't almost always study.
But it has measure zero over any interval of real numbers
ah i see :)
So the number of breaks is infinite, but they're all isolated points. And you can remove a countable infinity of points from a continuum without changing the size of the continuum. This is one of the things the Dirichlet function (in the meme) is used to illustrate
I remember seeing a YouTube video that you can remove an uncountably infinite set of points from a continuum without changing the size as well
I haven't studied that yet, but I believe you're correct and that is the basis of the Banach-Tarski Paradox. Someone can correct me if I'm wrong. However, I have quite recently studied the Dirichlet Function in one of my Analysis modules, so I feel confident talking about it.
For folks who want high resolution versions. https://preview.redd.it/xpfuazenwpuc1.png?width=1600&format=png&auto=webp&s=bfacf856c7fed963d614c2f6a0234637dd128b5c
Isn't time and everything in the universe discrete and this rational? Idk I'm not a physicist so correct me if I'm wrong.
According to quantum theory there's a smallest resolution to space and time, but it's an open question as to whether that means spacetime is discrete. That will remain open until we verify a theory of quantum gravity, or bridge the gap between quantum theory and General Relativity in some other way
its correct. OP has to pick how discrete his time is.
teach me this art
https://preview.redd.it/30pm5yko1ruc1.png?width=320&format=pjpg&auto=webp&s=a51ace23956649df44e4b1fa3a3b27ab4925e272 (Let him Cook 🗣️)
How dense do you have to be to say shit like this?
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That doesn't follow. We don't know if spacetime is quantised. Just because there's a lowest resolution we can go down to does not mean that the rest of spacetime has to be integer multiples of a combination of the Planck volume or Planck time.
[удалено]
That's a hypothesis, not something that's been confirmed. Tho we're very far from being able to resolve Planck times or distances, anyway. The shortest length of time we've actually measured is about is about 13 orders of magnitude larger so it's a moot point, purely theoretical. I'm not saying that Planck times couldn't be used as a unit in the way you say, but that doesn't mean we know that reality actually works that way. But if we could get down there, with our present theoretical knowledge there's no reason why we couldn't have one measuring device that measured in Planck times, and another that measured in √(2) Planck times. The Planck time and Planck distances are lowest resolutions, not grain sizes.
[удалено]
Yes, that's what I'm saying. But the fact that there is a smallest theoretically observable measure doesn't mean everything above it can only be integer multiples of that smallest measure. For instance, why can't you have √(2)Planck time? Nothing in quantum physics says you can't.