Infinity -- Cyclical?

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  • #26
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"Infinite" and "random" are different words with different meanings
So you can't have an infinite string of random digits?
 
  • #27
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You can, but not every infinite string has random digits.

An infinite string of random digits won't have anything repeating forever with probability 1.
 
  • #28
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So you can't have an infinite string of random digits?
I don't know if you can. Mathematically, an infinite string with random digits is very easily handled. Whether it exists in reality, or whether this mathematical result has any implications for reality, that can never be known.
 
  • #29
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I don't know if you can. Mathematically, an infinite string with random digits is very easily handled. Whether it exists in reality, or whether this mathematical result has any implications for reality, that can never be known.
Hmm something to think about.
 
  • #30
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So you can't have an infinite string of random digits?
I used to think that that is what an irrational number is after the decimal point, but it seems to be more complicated than that.

Alphabets or other non numeral representationscan be used to represent them, or other creative expressions that evaluate to them, useful things like series etc.

If by random you mean non repeating non terminating and not of a pattern.

. You are free to create any combination of symbols that represent numerals. The number exists, whether we are able to write it down or not "Type vs token" unless you will reject the fundamental notions and axioms.
 
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  • #31
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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
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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
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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
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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
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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 realise 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
jbriggs444
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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.
I enjoy a good philosophical debate, so I should be ok. I hope.
Somewhere else. Not here.
 

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