Is it possible that there is no geometrical infinity?

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    Geometrical Infinity
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Discussion Overview

The discussion revolves around the concept of geometrical infinity in relation to time, exploring whether the universe can be considered infinitely old or not. Participants examine the implications of infinite sets and sequences in the context of time, questioning the logical foundations of these ideas.

Discussion Character

  • Debate/contested
  • Conceptual clarification
  • Mathematical reasoning

Main Points Raised

  • One participant suggests that if time is represented as an infinite set, it complicates the understanding of specific sequences within that time, potentially implying that the universe is not infinitely old.
  • Another participant questions the meaning of a "sequence representing" time and emphasizes the importance of experimental evidence in validating mathematical models.
  • A different viewpoint argues that there is no mathematical impossibility in a universe that lasts forever, citing direct observation of a beginning and possibly an end.
  • Concerns are raised about determining reality based on models, with a participant stating that experiments are necessary to establish what is possible or impossible in the real world.
  • It is noted that having an infinite number of elements before and after a point in a sequence does not necessarily render the distance between those points ill-defined.
  • Participants discuss the ability to mark elements from an infinite sequence, suggesting that there are methods to choose or identify specific points within an infinite context.

Areas of Agreement / Disagreement

Participants express differing views on the implications of infinite time and the validity of models versus experimental evidence. There is no consensus on whether the universe can be considered infinitely old or the logical correctness of the initial claims.

Contextual Notes

Limitations include the dependence on definitions of infinity and sequences, as well as unresolved questions regarding the relationship between mathematical models and physical reality.

danov
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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?
 
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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?
 
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.
 
danov said:
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.
 

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