Does Infinity Exist in a Finite Reality?

Well, you are mixing more than one concept. The logical positivists would be giving you a scarlet M (for Metaphysik) to wear for using the word "exist", a metaphysical term.

But then you say a finite universe as an epistemological concept, which is quite a different type than metaphysics.

Now your question, if I understood it properly, is that if the universe is finite, how can we posit that infinity occurs nonvacuously?

1. We do not know if the universe is open or closed. Will it go on expanding or will it eventually contract once more to a super-atom? Well the calculations suggest we are between 20% and 98% short on mass for the eventual collapse, but perhaps that addiional matter is hidden in black holes. If the universe is open, then we have no problem with infinity because it will continue expanding.

2. Just because we can perceive and measure only four dimensions in this Universe does not mean those are the only ones that occur. String theory suggests otherwise, and we have mathematics capable of dealing with an infinite number of dimensions (e.g. Hilbert Spaces).

So, infinity occurs nonvacuously as an intellectual concept even though at this point in time, we cannot prove or disprove its occurrence in the reality of the senses.

Moreover, in the mathematics of the real number line, the numbers between 0 and 1 are in fact infinite. In fact, their infinity has a cardinality higher than the counting numbers {1, 2, 3,...} This can be proven in several simple ways but the proof by

Georg Ferdinand Ludwig Philipp Cantor is probably the easiest to understand. Check the link or find an elaboraation of it in E.W. Hobson's Theory of Functions of a Real variable.

It is not unusual to find intellectual realities which may or may not occur nonvacuously in the universe which we can measure with the senses. For example the square root of -1, the number i so that i*i = -1, is difficult to reconcile with this universe, but neverthe less the theory of analytic functions (that is, differentiable functions of a complex variable of the form x+i*y) is used by aeronautical engineers all the time to describe sources and sinks and the patterns of fluid flow.

So yes, infinity occurs nonvacuously, because it occurs in an intellectual reality. The number Pi, which is used in calculating the circumference of a circle and the area of it as well, is a non-repeating, non-terminating decimal which is not the solution to any algebraic equation. And Pi is very real. Radio and television and light would be nowhere without it.

What do you mean by "exist"? The numbers exist. The "number of numbers" is not finite (that is the original meaning of "infinite"). You cannot use a finite number to represent the number of numbers. The "infinitiness" of the number line is NOT pointing to ignorance. It is, to the contrary, pointing to the fact that we KNOW that there is no such thing as a "largest number". (And we -- humans -- have known this for over 2000 years, thanks to the Classical Greek geometers) Earth's surface (the 2-D portion) does not have an end, but it is not infinite: the length of the circumference (the distance you could go in a straight line before going over your starting point, roughly 40,000 km or 21,600 nautical miles) can be represented by a finite number -- depending on the unit used for the measurement. The universe appears to be boundless (no end), but we are not sure if it has a finite size. Note that the Observable Universe is finite (there is a distance beyond which it is impossible for us to perceive anything). Also note that spacetime -- a mathematical construct to represent the universe AND its history in one single mathematical model -- is also finite in one direction (the direction called "past" is finite in length) If the universe really is infinite in spatial extent, then infinites are possible. If the universe is isotropic (same properties in all directions) then an infinite universe should have an infinite number of just about everything (stars, planets, etc.). Because of the linear expansion of space, it is impossible for us to see an infinity of anything, even if that infinity does exist. However, to pretend that it can't exist just because we can't see it would be... ignorance. --- A "singularity" is a mathematical term which talks of a point (or a set of points) in a domain for an equation. It is a value, for the input variable, where the output of the function grows without bound. This is what people call (mistakenly) "infinite". [Because, frankly, unless you are deep in mathematics, there ain't much never mind between "infinite" and "without bound"] For example, this 3-dimensional function: f(x, y, z) = 1 / [(x-1)(y-2)(z-3)] has singularities at all locations where x = 1 (this is a 2-dimensional plane parallel to the y-z plane) y = 2 (this is a 2-dimensional plane parallel to the x-z plane) z = 3 (this is a 2-dimensional plane parallel to the x-y plane) The "singularity" is made up of three planes, each one perpendicular to the other two (like a radar reflector). The "singularity" is NOT a single point. When you work the equations of the Big Bang theory backwards, to find the energy density (a.k.a. temperature) of the universe at times in the past, you do reach a "singularity" which is a value of "t" (time) when the energy density grows without bound. THAT is the singularity. If, at that moment, the universe still has a non-zero size, then the singularity would apply to ALL the universe, everywhere at once. However, this "singularity" occurs at a time that happens to be before a moment we call the Planck Time. At the Planck Time (the energy density is still a finite number) the density is so high that we no longer understand how things work. Therefore, anything the theory tells us for "before" that moment (including the "singularity") is not reliable.

Infinity Exist

How can Infinity be reliant and space and time?

The World of infinity is so completely removed from any concept of reality that we currently have that none of our measuring systems (mathematics, physics, or philosophy) can come close to determining what it is, let alone understanding it.

At the most basic level of all matter, everything is interconnected. Think back in time, before the Big Bang, what was there? Was that level of existance depandant on space and time? That was the World of Infinity before everything in our reality broke apart and disconnected.

What we precieve in our limited five sences is space expanding, we see the evolution of our planet, and we see the evolution of you Human race. It makes you ask the question: why did we come out of that infinite space just to create the atom bomb?

We are at the lowest, dencest level of reality. We are so far removed from sencing our interconnection and the World of infinity we go around killing each other and pilaging nature because we don't realize it is all parts of ourselves.

The World of Infinity is the highest level of reality. There everything is perfectly connected above time and space and at complete rest. We are really there but we don't realize it. Everything decends from Infinity toward this world through increasing levels of concealment. Each level is like a seal and an inprint into the level below it.

So how do we realize we are in Infinity? We must accend back up through the worlds toward the complete interconnection of all things including ourselves. How do we do this? Only by realizing how disconnected we are from each other and then repairing what is broken.

Here are some links that further expalin Infinity:

http://www.illuzia.net/en/videos/clips/reality

http://perceivingreality.com/

http://www.kabbalah.info/engkab/kabbalah-video-cli...

I think you may be confusing yourself.

Infinity does exist, as you have stated, in maths/physics/ETC. However this doesn't instantly mean that the world will last for ever (or universe for that matter). There is no link to the mathematical definition of infinity and the probable prediction to when its all going to end.

The fact is we don't know when its going to end. But this isn't infinity, its uncertainty. You don't have to believe the world will last forever to comprehend the concept of infinity. You can just look at a picture of a circle for that.

I guess it depends on your definition of the word "infinity". As I understand it, it is a non-number used to represent something vanishingly large. As such, if one were to philosophize that the universe is temporally finite (that at some time it will cease to be), that is not to say it is spatially finite, though due to relativistic effects such as constraints on speed, this would put a crimp on how far one could travel in the time the universe were to exists.

Personally, I avoid "infinity" when dealing with maths, because (in most cases) it's the same as zero in that it's an approximation. It is much easier in general to manipulate what you're doing to avoid the issue.

An interesting point for sure.

You're assuming that a physical "infinity" can exist, but it can't. We can never physically or empirically confirm that something will never end. "Infinity" is purely a mental concept. It has nothing to do with the physical universe at all, so far as I can tell.

I'm not sure if anything you mention has anything to do with Platonic forms even in the most nominal sense.

Well, the fact is, we don't know that the universe WILL end. The Big Bang may eventually be followed by the Big Crunch, and the whole thing starts over again.

Also, we don't know that ours is the only universe. Many physicists postulate the existence of other universes in what is called the "Multiverse."

Infinity, or rather eternity, is beyond the realms of Earth life.

Although in mathematics and physics, you pose a very good question; One I can't say I have a decent answer for.

Well nobody knows the actual answer to this and i get very confused myself with it. And i don't understand how people can say it is going to end because how can they see into the future??

Nobody has been far enough into space to see if it stops somewhere.

But really good question it has gotten me thinking...x