Is Infinity Cyclical or Linear?

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Discussion Overview

The discussion revolves around the nature of infinity, specifically whether it is cyclical or linear. Participants explore concepts related to the representation of numbers, the properties of infinity, and the implications of using different numerical bases. The conversation includes theoretical considerations and speculative reasoning.

Discussion Character

  • Exploratory
  • Debate/contested
  • Conceptual clarification
  • Mathematical reasoning

Main Points Raised

  • One participant suggests that infinity must eventually return to previously used numbers, raising the question of whether infinity is cyclical or linear.
  • Another participant asserts that one never "runs out of numbers," emphasizing that 1234 is not infinity and that infinity cannot be represented as a finite integer.
  • There is a discussion about the nature of digits and how, in any finite string of numbers, digits will eventually repeat.
  • Some participants argue that while you can write an unending string of numbers, it is false to claim that you will eventually write down every possible unending digit string, referencing Cantor's proof.
  • There are comments on the limitations of numerical bases, with a participant noting that you cannot have an infinite base and that new symbols would be needed for bases greater than 10.
  • One participant expresses confusion about the concept of infinity having no digits, questioning how it can be represented numerically.
  • There is a proposal to explore the representation of numbers in non-integer bases, such as the square root of two, and whether rational and irrational bases can be used in a coherent system.

Areas of Agreement / Disagreement

Participants express differing views on the nature of infinity and its representation, with no consensus reached on whether infinity is cyclical or linear. The discussion includes multiple competing ideas and unresolved questions regarding numerical representation and the properties of infinity.

Contextual Notes

Participants acknowledge limitations in their understanding and express uncertainty about the implications of their arguments. There are unresolved mathematical concepts related to the representation of numbers in various bases and the nature of infinity itself.

  • #31
Bipolar Demon said:
If by random you mean non repeating non terminating and not of a pattern.
That's exactly what I meant by random. Thanks for the explanation. I shall read further into it.
 
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  • #32
BL4CKB0X97 said:
That's exactly what I meant by random. Thanks for the explanation. I shall read further into it.

You shall not do so without having to encounter some kind of philosophy.:nb):smile:
 
  • #33
Bipolar Demon said:
You shall not do so without having to encounter some kind of philosophy.:nb):smile:
I enjoy a good philosophical debate, so I should be ok. I hope. [emoji2]
 
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  • #34
Bipolar Demon said:
You shall not do so without having to encounter some kind of philosophy.:nb):smile:
How so? In a random number, each digit that appears has an equally likely chance. So in, say, the fourth place, a 1 digit is as likely as a 2 digit, or 3 digit, and so on. Not much philosophy there that I see.
 
  • #35
Mark44 said:
How so? In a random number, each digit that appears has an equally likely chance. So in, say, the fourth place, a 1 digit is as likely as a 2 digit, or 3 digit, and so on. Not much philosophy there that I see.
Yes, one can reduce such a number to an random algorithm, you are right.

I was under the (possibly wrong) impression such an investigation would lead one to ask questions like

"What is number?" "what is infinity?" "do we have anything infinite in the universe?" and come up across some general philosophy of mathematics and views of people who say that the irrational number and other infinite objects do not exist and should be discarded, then the OP will perhaps investigate the philosophy behind such peoples views. I think OP will then realize that although the basic principles were inspired by reality and nature, the results and relationships that arise are outside of space and time.:redface:
 
  • #36
Bipolar Demon said:
Yes, one can reduce such a number to an random algorithm, you are right.

I was under the (possibly wrong) impression such an investigation would lead one to ask questions like
[snip possible philosophical musings]
One can speak of randomness, irrational numbers, infinite quantities and infinite sets without venturing at all into philosophy. This is good since philosophy is not acceptable subject matter here.
BL4CKB0X97 said:
I enjoy a good philosophical debate, so I should be ok. I hope.
Somewhere else. Not here.
 

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