I don’t give a damn about infinity. If it is doable, why not? But is it? That’s the only question.
Then, a supertask mixes the infinite set of naturals and we are witnessing “the irresistible force acting on an unmovable object”. What the Hell will happen? Will we have finite numbers on the first 1000 places? We should, but bigger, no matter which will be.
The “irresistible force” is just an empty word. And so is “unmovable object”. And so is “infinity” and so is “supertask”.
Empty words. So every theory which encompasses them is flawed. More than likely.
There is an argument there, but it certainly is not one based on ZFC, since no axiom of set theory says anything about time or what can be accomplished in time.
Physics is built on top of mathematics, and almost all of mathematics can be built on top of ZFC (there are other choices). But there is as much time in ZFC as there are words in a single pixel on your screen.
I don’t give a damn about infinity. If it is doable, why not? But is it? That’s the only question.
I’m not sure what you mean by this, especially given your earlier focus on whether infinity exists and whether using it in physics is akin to religion. I’m also not sure what “it” is in your sentence, but it seems to be the supertask in question. I’m not sure in that context what you mean by “doable.”
Then, a supertask mixes the infinite set of naturals and we are witnessing “the irresistible force acting on an unmovable object”. What the Hell will happen? Will we have finite numbers on the first 1000 places? We should, but bigger, no matter which will be.
The “irresistible force” is just an empty word. And so is “unmovable object”. And so is “infinity” and so is “supertask”.
I’m not at all sure what this means. Can you please stop using analogies can make a specific example of how to formalize this contradiction in ZFC?
This seems to be essentially the same argument and it seems like the exact same problem: an assumption that an intuitive limit must exist. Limits don’t always exist when you want them to, and we have a lot of theorems about when a point-wise limit makes sense. None of them apply here.
I don’t think this conversation is being very productive so this is likely my final reply.
Just answer me a simple question.
? How do the first 1000 naturals look like, after mixing supertask described above has finished its job,
You may say that this supertask is impossible.
You may say that there is no set of all naturals.
The resulting pointwise limit exists, and it gives each positive integer a probability of zero. This is fine because the pointwise limit of a distribution on a countable set is not necessarily itself a distribution. Please take a basic real analysis course.
I don’t give a damn about infinity. If it is doable, why not? But is it? That’s the only question.
Then, a supertask mixes the infinite set of naturals and we are witnessing “the irresistible force acting on an unmovable object”. What the Hell will happen? Will we have finite numbers on the first 1000 places? We should, but bigger, no matter which will be.
The “irresistible force” is just an empty word. And so is “unmovable object”. And so is “infinity” and so is “supertask”.
Empty words. So every theory which encompasses them is flawed. More than likely.
And yes, supertask can be established in ZFC.
The topic is also exercised here:
http://mathforum.org/kb/thread.jspa?forumID=13&threadID=2278300&messageID=7498035
There is an argument there, but it certainly is not one based on ZFC, since no axiom of set theory says anything about time or what can be accomplished in time.
So you say, ZFC has nothing to do with time? Time in physics is uncovered in ZFC?
Physics is built on top of mathematics, and almost all of mathematics can be built on top of ZFC (there are other choices). But there is as much time in ZFC as there are words in a single pixel on your screen.
I’m not sure what you mean by this, especially given your earlier focus on whether infinity exists and whether using it in physics is akin to religion. I’m also not sure what “it” is in your sentence, but it seems to be the supertask in question. I’m not sure in that context what you mean by “doable.”
I’m not at all sure what this means. Can you please stop using analogies can make a specific example of how to formalize this contradiction in ZFC?
This seems to be essentially the same argument and it seems like the exact same problem: an assumption that an intuitive limit must exist. Limits don’t always exist when you want them to, and we have a lot of theorems about when a point-wise limit makes sense. None of them apply here.
Just answer me a simple question.
How do the first 1000 naturals look like, after mixing supertask described above has finished its job,
You may say that this supertask is impossible.
You may say that there is no set of all naturals.
Whatever you think about it. Everything else is pretty redundant.
I don’t think this conversation is being very productive so this is likely my final reply.
The resulting pointwise limit exists, and it gives each positive integer a probability of zero. This is fine because the pointwise limit of a distribution on a countable set is not necessarily itself a distribution. Please take a basic real analysis course.