Is Infinity Cyclical or Linear?

  • Context: High School 
  • Thread starter Thread starter BL4CKB0X97
  • Start date Start date
  • Tags Tags
    Infinity
Click For Summary
SUMMARY

The discussion centers on the nature of infinity, questioning whether it is cyclical or linear. Participants clarify that infinity is not a number and cannot be expressed in finite terms, using examples such as Cantor's diagonal argument to illustrate that infinite sequences do not necessarily repeat. The conversation highlights the misconception that one can "run out of numbers" within an infinite context, emphasizing that infinity encompasses all conceivable numbers without repetition. Ultimately, the consensus leans towards infinity being linear rather than cyclical.

PREREQUISITES
  • Understanding of Cantor's diagonal argument
  • Basic knowledge of infinite sequences and series
  • Familiarity with mathematical concepts of linearity and cyclicity
  • Awareness of the eternal recurrence concept in philosophy and mathematics
NEXT STEPS
  • Study Cantor's diagonal argument in detail
  • Explore the concept of infinite sequences in mathematics
  • Research the eternal recurrence theory and its implications
  • Investigate the differences between finite and infinite sets in set theory
USEFUL FOR

Mathematicians, philosophers, students of mathematics, and anyone interested in the theoretical implications of infinity and its properties.

  • #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.
 
  • Like
Likes   Reactions: Logical Dog
Mathematics news on Phys.org
  • #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]
 
  • Like
Likes   Reactions: Logical Dog
  • #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.
 

Similar threads

  • · Replies 5 ·
Replies
5
Views
8K
  • · Replies 7 ·
Replies
7
Views
3K
  • · Replies 31 ·
2
Replies
31
Views
3K
  • · Replies 11 ·
Replies
11
Views
5K
  • · Replies 13 ·
Replies
13
Views
4K
  • · Replies 8 ·
Replies
8
Views
3K
  • · Replies 10 ·
Replies
10
Views
5K
  • · Replies 20 ·
Replies
20
Views
3K
Replies
2
Views
2K
  • · Replies 14 ·
Replies
14
Views
30K