Originally posted by googlefudge Nope, sorry that wont do.
Turns out the world is more complicated than they taught you at age 5.
Hmm...I actually think Chesspraxis's first offering, though equipped with redundancy (no need for "unlimited" ), captures the essence of infinity quite well. That which is characterised by boundlessness is what it means to be infinite. It may well be missing some of the more esoteric mathematical nuance but for conveying the basic principle it does the job.
Similarly, a box is characterised by it's ability to contain things; the nuance is in the many different types of boxes.
Originally posted by Agerg Hmm...I actually think Chesspraxis's first offering, though equipped with redundancy (no need for "unlimited" ), captures the essence of infinity quite well. That which is characterised by boundlessness is what it means to be infinite. It may well be missing some of the more esoteric mathematical nuance but for conveying the basic principle it does the job.
S ...[text shortened]... rised by it's ability to contain things; the nuance is in the many different types of boxes.
Apart from the fact that I can think of uses of infinity that are bounded. (rational's between 1 and 2 for example)
Also the entire thread is about nuance and detail.
Originally posted by googlefudge Apart from the fact that I can think of uses of infinity that are bounded. (rational's between 1 and 2 for example)
Also the entire thread is about nuance and detail.
But the number of such rationals *is* unbounded; indeed only the bit that pertains to infinity in this example is a "quantity" of rationals. As such boundlessness applies.
As for nuance, I get the impression that's optional for those with sufficient background - and that "layfolk" are not barred from participitation.
One that is exceptionally difficult to fully grasp.
The question in the op is a perfectly reasonable one.
Do you have anything relevant to say, or are you just here to snark at people who want to
increase there understanding of the world?
Infinity may be a "complicated mathematical concept," but it's essence is quite simple. It IMO is our own finite minds that limits the undestanding of what we can't really imagine.
I'm here to learn and try to inform. I'm sorry if that makes you uneasy, but then for me at least, that privilege has been paid for.
Originally posted by Agerg Hmm...I actually think Chesspraxis's first offering, though equipped with redundancy (no need for "unlimited" ), captures the essence of infinity quite well. That which is characterised by boundlessness is what it means to be infinite. It may well be missing some of the more esoteric mathematical nuance but for conveying the basic principle it does the job.
S ...[text shortened]... rised by it's ability to contain things; the nuance is in the many different types of boxes.
Originally posted by googlefudge Apart from the fact that I can think of uses of infinity that are bounded. (rational's between 1 and 2 for example)
Also the entire thread is about nuance and detail.
When I first grasped it, I was looking at my ruler, I divided it into 2- 6 in, then 4- 3 in. After I had worked it down to one 16th of an inch, the divisions on the ruler quit, but I knew it would be 1/32...1/64...1/128 and so on. It occured to me that it would go on forever. Infinity produced from a finite space, somehow it clicked.
I love your example of rationals, spot on.
There are two completely independent throws and entities being dealt with here. One is the infinity of numbers, and the other the infinity of space.
Infinity, by itself, is a paradox that the human brain, mostly, is untrained to cope with. We are conditioned to think with space that there is always more space, because we live in a small space that has boxes outside of the smaller boxes. That's how our logic and ability to cope with space has developed.
In my opinion the universe/s is/are all within one expanding and retracting (in different areas simoultaneously) effective balloon of space. It is never ending but encapsulated, if you can grasp that. What's outside of it? NOTHING. There is no outside, and that's the difficulty the brain has in visualising, because of our pre-conditioning from our space experience. The balloon is infinite, because which everway you travel you will eventually come back to the same place if you follow the boundary (Mind that would take longer to do than the universe has been in existence 😀!).
Numbers also have a limit. If you read about Graham's number and so forth, and the reasons why it is so large and can't get bigger, then mathematically it makes sense. The layman would just argue that I can have Graham's number + 1. Well you can't, because the +1 part is already included in the original number. It can't expand. And that's another difficult thing for the human concept, because we 'think' we can have something and simply add 1 to it. Not correct!
-m.
Edit: apologies I mean't Graham's number. Alexander's number refers to knots, but is still very interesting also.
Originally posted by mikelom There are two completely independent throws and entities being dealt with here. One is the infinity of numbers, and the other the infinity of space.
Infinity, by itself, is a paradox that the human brain, mostly, is untrained to cope with. We are conditioned to think with space that there is always more space, because we live in a small space that has box 's number. Alexander's number refers to knots, but is still very interesting also.
We believe that the universe is governed by Einstein's theory of general relativity, which among other things addresses such matters as the overall structure of the universe.
In the early 1920s Alexander Friedmann showed that using one assumption (homogeneity - the universe has roughly the same density everywhere), the equations of general relativity can be solved to show that a finite universe must have a larger density of matter and energy inside it than an infinite universe would have.
There is a certain critical density that determines the overall structure of the universe.
If the density of the universe is lower than this value, the universe must be infinite, whereas a greater density would indicate a finite universe.
These two cases are referred to as an open and closed universe respectively.
The critical density is about 10-29 g/cm3, which is equivalent to about five hydrogen atoms per cubic meter.
In comparison the density of water is roughly 1 g/cm3 or about 500 billion billion billion hydrogen atoms per cubic meter.
However, we live in a very dense part of the universe.
Most of the universe is made up of intergalactic space, for which a density as low as the critical density is plausible.
So we should be able to answer the question of the universe being infinite or finite by measuring the density of everything around us and seeing whether it is above or below the critical value.
The problem is that the measured density turns out to be pretty close to the critical density.
Right now the evidence seems to favor an infinite universe, but it is not yet conclusive.
To quote myself from page two.
Sorry to say, but your "veiw" is just as much a belief as any religion. In other words, it isn't proven whether or not the universe is infinite; besides that, if you came back to the same place it would not be an infinite space.
Edit: And you can add 1 to Graham's number. The only special thing about Graham's number was that at one point it was the largest number used in a serious mathematical proof but since then larger bounds have appeared. Read up on Kruskal's Theorem... there is a link below.
It would be considered by people to be non-infinite because it has an end? That's the whole point. Infinity can go on forever but have boundaries, that is what I alluded to.
I am aware of the newer mathematical concepts, and only referred to Graham's number because it is well known and there is much written about it with simple explanation.
My point again is, as per above, that infinity has boundaries, and doesn't just expand or arithmetate forever.
Originally posted by mikelom I did say 'In my opinion'.
It would be considered by people to be non-infinite because it has an end? That's the whole point. Infinity can go on forever but have boundaries, that is what I alluded to.
I am aware of the newer mathematical concepts, and only referred to Graham's number because it is well known and there is much written about it with simp ...[text shortened]... above, that infinity has boundaries, and doesn't just expand or arithmetate forever.
-m.
Well, it would be infinite in the respect that you can travel infinitely and that it is unbounded because it is the whole that we are part of.
IMO It is easier to conceptualize the universe as bounded than it is to conceptualize it as unbounded but I can see what you mean in your post. I mainly wanted to avoid confusion from others as your post seemed pointed towards those who are in-between lay persons and ones aquainted with these concepts.
Originally posted by mikelom There are two completely independent throws and entities being dealt with here. One is the infinity of numbers, and the other the infinity of space.
Infinity, by itself, is a paradox that the human brain, mostly, is untrained to cope with. We are conditioned to think with space that there is always more space, because we live in a small space that has box 's number. Alexander's number refers to knots, but is still very interesting also.
Numbers also have a limit. If you read about Graham's number and so forth, and the reasons why it is so large and can't get bigger, then mathematically it makes sense. The layman would just argue that I can have Graham's number + 1. Well you can't, because the +1 part is already included in the original number. It can't expand. And that's another difficult thing for the human concept, because we 'think' we can have something and simply add 1 to it. Not correct!
weirdly I came across Knuth\'s arrow notation quite randomly about a month ago when I was musing over tetration and pentation with a friend
. Knuth's arrow notation defines iterated exponentiation - and so for any positive integer > 1, and finitely many arrows, the resulting expression is well defined and finite. As such, for Grahams number = G, then G < G+1 is definitely true, and furthermore not only is it the case that the +1 is not included in the original number, but it can be made a hell of a lot bigger (for example take it's factorial).
Originally posted by josephw Infinite blah blah blahs.
[b]Infinite. The opposite of finite. Finite=numerable. Infinite=innumerable.
Sometimes I think you guys just like to think something is more complicated than it really is.
Maybe somethings are just too simple for you to understand. idk[/b]
I dont know if the "infinite" has any opposites because by definition it contains everything/alltime ,so you cant put something finite up against that and say it is it's opposite. Maybe on paper, but in reality it is not it's opposite.
Take a finite no. like 5. Whats the opposite of 5? -5?
It's certainly not infinity.
Originally posted by googlefudge Agerg will probably answer this better, but sometimes different explanations in concert help make things easier to understand.
Of course it is possible that it will just confuse things further but hey ho ;-)
It has to do with there being classes of infinity.
The lowest/smallest of which being what's called the countably infinite.
Countable infi ...[text shortened]... t with as non-technical as possible
as I suspected you would go down the technical route)
And you can postulate number lines from each of those numbers going off in other dimensions, even the three physical ones we have would introduce yet another level of infinities. You could have an infinite number of number lines protruding from any point on the original one dimensional number line.
Originally posted by karoly aczel I dont know if the "infinite" has any opposites because by definition it contains everything/alltime ,so you cant put something finite up against that and say it is it's opposite. Maybe on paper, but in reality it is not it's opposite.
Take a finite no. like 5. Whats the opposite of 5? -5?
It's certainly not infinity.
Wouldn't that just be 1/5, inverse of 5? 1/infinity?
Infinity: Philosophical Considerations
13 Oct '11 22:292 edits
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