Is it possible that there is no geometrical infinity?

[danov]

Lets imagine following:

We have an infinite set of numbers representing the time.
Now if we want to know how much time has spent in a specific sequence of this infinite set we see that this is impossible because there is infinite time passed before this sequence and infinite time passed after it because infinite set has no end.

This would i.e. mean that our world (the unvierse, or something our universe is included into) is not infinite(ly) (old). Because we do have time "sequences".

Contrary to that:

If we imagine infinite time as infinite line. This line might be infinite but contrary to the infinite number set we could "see" sequences on it i.e. by making to marks in some distance on this infinite line.

This would mean that our world might be infinite(ly) (old).

What are the logical mistakes / wrong conjectures I am making?

 

[HallsofIvy]

I'm sorry, what do you mean by a sequence "representing" time? The fundamental "logical" error is that no mathematical model is any better than the experimental evidence the model is based on. What experimental evidence is yours based on?

 

[Alex6200]

Your logic doesn't follow. There is nothing mathematically impossible about a universe that lasts forever, it's just that direct observation shows that there is a beginning and (methinks) an end.

 

[CRGreathouse]

What are the logical mistakes / wrong conjectures I am making?

"Now if we want to know how much time has spent in a specific sequence of this infinite set we see that this is impossible"

1. You can't determine what is possible or impossible in the real world based on a model. Experiments in the real world are required.

"because there is infinite time passed before this sequence and infinite time passed after it because infinite set has no end."

2. Just because a sequence has an infinite number of elements before some point, and continues infinitely after some other point, doesn't mean that the distance between the two is ill-defined.

"Because we do have time 'sequences'."

3. This statement confuses the real world with its models.

"If we imagine infinite time as infinite line."

4. As #1, you can't determine reality from a model.

"This line might be infinite but contrary to the infinite number set we could "see" sequences on it i.e. by making to marks in some distance on this infinite line."

5. There are ways of choosing/"marking" elements from an infinite sequence.

"This would mean that our world might be infinite(ly) (old)."

6. As #1.