Infinity

[KALSTER]

This seems to be a widely misunderstood concept (including by me), yet one commonly used wrongly. One of the common mistakes, for instance, is describing something as simply infinite without specifying exactly what quality of the thing is supposed to be infinite. So let me make some statements and ask some questions regarding infinity and I would like anyone properly knowledgeable to verify their validity, if not make some corrections.

 

It seems to me that structure can exist within infinity. One example of this would be that in a hypothetical universe that is infinite in time, space and matter, that matter could exist as one particle per light year or as an infinite gas cloud and that both scenarios would have infinite matter.

 

As I understand it, it is considered in mathematics that 0.99999..... = 1. But does this necessarily have to be the case in reality? If you have an infinite data set where 0.99999..... is supposed to describe the probability of a certain property to be exhibited by each element of the data set, does that mean that among any number of elements in the infinite data set you would care to consider that all of them would exhibit this particular property? (hope that was coherent :? )

 

Am I wrong though in saying that limits are only a way for us to deal with infinity? It involves choosing an infinitesimal that has to be added after a certain number of iterations of the series, no? The smaller the infinitesimal the more accurate the result that is attained. In reality you could reduce the size of the infinitesimal infinitely, ending up right back where you started. Or do I misunderstand something?

[Yuri Danoyan]

Just in case: http://books.google.com/books?id=cU3HQFek7L0C&dq=vilenkin+infinity&source=gbs_summary_s&cad=0

[Mr Skeptic]

Well, for one thing, .9999999... = 1 = 9/9 = one = uno = any other name you have for one. Yes, that has to be the case as it has been proven. You can look that up, as there are proofs everywhere including this forum. In math, when you prove something, it has to be true given that the assumptions you start with are true. However, numbers don't necessarily exist in reality, but we use them to describe reality.

 

As for your comment on infinity... Yes, in math it is pretty much only used for limits. In set theory they use infinities, but they have more specific infinities than just "infinite".