untermensche
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That is a set with endless elements. There is no last one. There is no end. There may be a highest limit.
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What does it mean for something to be "logically possible"?
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That is a set with endless elements. There is no last one. There is no end. There may be a highest limit.
bilby
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What the FUCK is wrong with you? This isn't a pissing competition; I don't need (nor intend) to derive all of mathematics from scratch, because others have already done the work. I am happy to rely on people who are smarter than me, because I recognize that no one person can possibly learn a worthwhile fraction of what there is to know without help from others - most of whom are long dead. I suppose you would look at Sir Issac Newton's comment about 'standing on the shoulders of giants', and say "You can't explain one thing on your own can you, Issac?"
Why? It's been shown to you twice. Why the fuck would pointing it out a third time make it sink in?
bilby
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It is abundantly clear that nobody can show you anything that doesn't fit with your preconceptions.
untermensche
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Never made the claim. You can't show me anywhere I did.
The integers consist of three sets and this was explained.
The positive integers. The negative integers. And zero.
Zero is not positive or negative and not part of the set of the positive or negative integers.
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You show no ability to be skeptical about extraordinary claims.
You are the type who can be made to believe anything.
beero1000
Veteran Member
I wonder what he would do with a set like "all the rational numbers greater than √2". Where's the beginning?
untermensche
Contributor
I said "series".
You have to learn to read.
I said every series has a beginning. We are talking about time after all. If you claim you have a series then you have a first element.
You can't define an infinite series without defining the first element.
If you want to progress you have to progress from something.
Going from nothing to nothing is not progression. Going from nothing to something is not possible. (the other side of the paradox that some don't seem to like)
Kharakov
Quantum Hot Dog
No rational number is greater than the square root of 2. I mean, well, you're sort of treading on my personal feelings about the square root of 2.
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untermensche
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Looks like the square root of 2 to the double prime.
If you are using a greater than proposition you really have two infinite segments.
To define each infinite segment you can pick an arbitrary point but you have to start the series somewhere to have an infinite series.
You cannot begin a series from "the undefined" or "the non-existent".
untermensche
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An infinite series must have a defined first element. Try to build one without one.
None of this has anything to do with time however which cannot be divided infinitely.
It is impossible for there to have been infinite time in the past.
It is impossible for the time in the past before any given time to be infinite.
Infinite time cannot occur BEFORE anything. It is time that goes on and on. It can only keep occurring. It cannot have occurred.
bilby
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No.
What makes you imagine that such a series must be 'built'? What does 'build' even mean here?
How do you know this?
You don't know this. You just believe it.
You don't know this either.
This is not even coherent.
If the past is infinite, then infinite time not only can, but MUST have occurred before any point in time.
You do not, despite your emphatic claims, know whether or not the past is infinite. But if it is, then infinite time has, by definition, passed. And it has had an infinite amount of time in which to do so, so there's nothing logically impossible about this whatsoever.
beero1000
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Now you're a stickler for using correct terminology? I have no idea what you mean by "series". It certainly isn't the well accepted and understood mathematical definition though, and it seems to vary depending on what properties you wish your "series" to have.
Anyway, the set of rational numbers greater than the square root of 2 is an ordered collection of numbers. You've claimed that if something has an order that implies a beginning. So here we are...
untermensche
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None of that makes it possible for an infinite amount if time to ever finish. Not even if it has infinite time.
It doesn't finish.
It can't be in the past.
The past must be finite therefore.
It doesn't finish.
It can't be in the past.
The past must be finite therefore.
bilby
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Why not? Given infinite time, any amount of time can pass.
The past finishes now; and that remains true whether or not the past is infinite; and whether or not you like it.
Where else can it be?
Therefore my arse. You don't get a 'therefore' until you give us some sound reasoning.
untermensche
Contributor
Infinite time is not an amount of time.
It is by definition time that never finishes.
It cannot finish. No matter how much time it has it will not finish.
It is not something that can be in the past.
Which is proof it could not have been infinite.
Infinite time never finishes.
beero1000
Veteran Member
*crickets*
untermensche
Contributor
I already explained this to you.
If you want to depict some "greater than" relation you actually have to create two series of numbers. You also have to stipulate that a point has no dimension, thus separating yourself permanently from the real world.
You can begin them at any point contained within the set. They are all an equal number of elements from the "start" and the "finish".
A series needs a first element.
You cannot have a series of elements that begins from "the undefined" or the "the non-existent".
But this is meaningless trivia.
What is of importance is the idea that an infinite series is by definition a series that does not end.
There is no last element. There can be no last element. By definition.
beero1000
Veteran Member
Basically every statement here is wrong. It's scary how you think you're actually making sense.
Maybe you're using some alternative definition of 'explained' here, because no, you haven't.
So now you're saying I can't say one number is greater than another unless I create TWO 'series' of numbers? Extraordinary. How do I use these two series to depict some "greater than" relation?
If I can begin anywhere, then isn't your 'beginning' arbitrary and useless? Kind of like you're defining one just so you can say you have one? Y'know, to avoid losing face by admitting that your ridiculous claims might not be completely correct?
Still unclear on what you think a 'series' actually is...
You got the meaningless part right.
Whose definition? What definition? I haven't seen one yet.
Maybe you're using some alternative definition of 'explained' here, because no, you haven't.
So now you're saying I can't say one number is greater than another unless I create TWO 'series' of numbers? Extraordinary. How do I use these two series to depict some "greater than" relation?
If I can begin anywhere, then isn't your 'beginning' arbitrary and useless? Kind of like you're defining one just so you can say you have one? Y'know, to avoid losing face by admitting that your ridiculous claims might not be completely correct?
Still unclear on what you think a 'series' actually is...
You got the meaningless part right.
Whose definition? What definition? I haven't seen one yet.