But it’s impossible for to construct a smallest possible distance (1/infinity) - we can merely construct successfully smaller distances in a process that tends to but never reaches 1/infinity. That’s the definition of potentially infinite. I asked for an example from nature that is actually infinite... — Devans99
There's no "constructing" here, space is just infinitely divisible. There's no such thing as a smallest possible distance. — MindForged
Well, actually in physics, space does not seem to be infinitely divisible. — LD Saunders
that gives us a good reason for thinking of space and time as a continuum and no good reason for thinking otherwise. — SophistiCat
The definition of infinity is pretty clear, it's extremely useful in mathematics and science, and it introduces no contradictions into the theorems. — MindForged
That is a misuse of the word 'so'. The word is used after a deduction has been presented, to state the result of the deduction. It is invalid to use it to just state a new assertion that bears no relation to previous assertions, which is what has happened here.Yes; so an object with no start is a non-existent object; — Devans99
Amen, comrade!I never look up links referenced during a discussion. This is for two reasons: 1. Any nonsense can be posted on the web, and often is. 2. If someone has an argument to make, then they should be able to state it in their own words. — LD Saunders
While almost all approaches to quantum gravity bring in a minimal length one way or the other, not all approaches do so by means of “discretization”—that is, by “chunking” space and time. In some theories of quantum gravity, the minimal length emerges from a “resolution limit,” without the need of discreteness. Think of studying samples with a microscope, for example. Magnify too much, and you encounter a resolution-limit beyond which images remain blurry. And if you zoom into a digital photo, you eventually see single pixels: further zooming will not reveal any more detail. In both cases there is a limit to resolution, but only in the latter case is it due to discretization.
In these examples the limits could be overcome with better imaging technology; they are not fundamental. But a resolution-limit due to quantum behavior of space-time would be fundamental. It could not be overcome with better technology.
http://www.pbs.org/wgbh/nova/blogs/physics/2015/10/are-space-and-time-discrete-or-continuous/
That's an interesting idea. If I'm reading you correctly, you're suggesting that there is some point in the universe, call it C (for centre), such that, as we approach a certain number of km from C, we find our movements increasingly constrained and, as we continue, increasingly slowly, we asymptotically become paralysed. It's like there's some kind of sticky force field in the universe that grows stronger and stickier as we move away from C.It’s a problem I agree but I can think of a way past 2 above: imagine as you get closer to the edge of the universe time slows down and right at the edge time stops. So it’s impossible to poke a spear through the edge of the universe because there is no space time in which to poke the spear. — Devans99
...imagine as you get closer to the edge of the universe time slows down and right at the edge time stops. So it’s impossible to poke a spear through the edge of the universe because there is no space time in which to poke the spear. — Devans99
We can’t conceive of logically inconsistent concepts like Actual Infinity in a logically consistent way.
I’d allow for the existence of the inconceivable only if it where possible. No need to allow for impossibilities like Actual Infinity. — Devans99
A set is infinite if it's members can put into a one-to-one correspondence with a proper subset of itself. So we know the natural numbers are infinite because, for example, there's a function from a set to a proper subset (read: non-identical) of itself like the even numbers. For every natural number, you're always able to pair it up with an even number and there's no point at which one of the subset cannot be supplied to pair off with the members of the set of naturals.
That's pretty clear, it's exactly the same reason I can, without knowing the exact number of people in an audience, know that if every seat is occupied, then there's no empty seats (each seat can be paired off with a person). — MindForged
I see no clear definition of infinity here, just a rambling description of a particular type of set, which you call an infinite set. That description doesn't tell me what it means to be infinite, it tells me what it means to be an infinite set. — Metaphysician Undercover
As has been said a few times, several very solid theories make assumptions that include infinity. — MindForged
How this is rambling, I don't know. It's literally just lining things up. — MindForged
And you have been reminded a few times that these solid theories in fact depend on working around the infinities they might otherwise produce. So it ain't as simple as you are suggesting. — apokrisis
Instead of being fundamental, the perfect regularity and simplicity of a classical geometry is the most exceptional case. It requires a lot of explanation in terms of what removes all the possible curvature, divergence, and other non-linearities. — apokrisis
You have demonstrated that the set of natural numbers is equivalent (in the sense of having the same number of members) as the set of even numbers. That's nonsense, and that's what the concept of infinity introduces into mathematics, nonsense. — Metaphysician Undercover
It's nonsense because it's a totally useless piece of trivia. Infinite sets have the same number of members as other infinite sets ... a nonsense number ... an infinite number. — Metaphysician Undercover
Nonsense based on what argument? — MindForged
The infinite set is specifically designed for no reason other than to break this law, therefore it is unreasonable, nonsense. — Metaphysician Undercover
As it is an unbounded (open) set, it is not truly a "set", as a collection of objects, it is a boundless collection which is not a collection at all. — Metaphysician Undercover
A collection, or "set" means that the members are collected together in a group. If the collecting is not complete, then the described collection (set) does not exist. To call it a collection, or set, is contradictory nonsense. — Metaphysician Undercover
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