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I have some confusion between with resolving the following situation.

I know that no measurable quantity can have a value of infinity. For example, I just wrote something out, but clearly this doesn't work, since infinity is not really a number and thus measurable entities can't be quantified as being of infinite amount.

I own an infinite amount of coins scattered on the ground. I give you all of them so I have none left and you have an infinite amount.

With the same infinite amount of coins, you then give me all coins showing heads, and keep all coins that are tails. Now we both have an infinite amount of coins.

I then keep £100 worth of coins for myself and give the rest back to you.

Does that then mean that you have made a net gain of coins, or do you have the same amount of coins as you had before?

I can understand that the above doesn't make sense, however, what if you were to use the same concept with time.

For example, if I ask this question:

Is time infinite?

I can't understand how the answer to that can be either Yes or No. Both answers must be wrong.

If you respond saying yes, and say that time is in fact infinite, then it would mean that up until the writing of this question, that an infinite amount of time has past, and that an infinite amount of time is still yet to pass. However, the fact that I am writing this post now, must mean that time is not infinite, because how can an infinite amount of time have already past, if I am writing this now?

Put simply, "now" cannot exist, if time is infinite.

Equally, if you were to respond and say "no" time is not infinite, then that would mean that the big bang started time, but then that must also mean that time needs to stop at some point. Otherwise, time would be again be infinite, meaning that "now" could never exist.

(Someone feel free to change the title of this question to something more suitable).

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closed as off topic by David Z Sep 7 '11 at 21:21

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you're first thought is somewaht akin to Hilberts' Grand Hotel's_paradox_of_the_Grand_Hotel . Also I don't understand why when tie is infinite, you can conclude that it is infinte in the past and future. The set of positive numbers are infinite, but still habe a beginning. – luksen Sep 7 '11 at 21:19
Hi Layke - welcome to Physics Stack Exchange! Unfortunately your question ("how can an infinite amount of time have already past, if I am writing this now?"), as far as I can tell, is philosophical (not physical) in nature; it's not based on accepted science, which makes it off topic here. There is a Philosophy site, although I don't know if this question is precise enough to be on topic there. If you like, we could discuss how to improve your question, and possibly bring it on topic, in Physics Chat. – David Z Sep 7 '11 at 21:20
That's okay David. I had imagined that it would probably get closed. And thanks for the link luksen. – Layke Sep 7 '11 at 21:50
I found this question to be interesting. It is as philosophical as "is the universe infinite". – Jus12 Sep 7 '11 at 22:42
@Layke: thanks for understanding. Hopefully I didn't scare you away from the site ;-) – David Z Sep 8 '11 at 2:00