[evan_au]

if its a infinity then its an infinity, right?

I'm afraid not. There are infinities, and then there are bigger infinities.

In general, 2^∞ > ∞

See: https://en.wikipedia.org/wiki/Aleph_number

[yor_on]

Well yes. but if I take the smaller 'infinity' and put it into the 'bigger'
It should still fit, right? :)

Because if not, you just invalidated the logic
Actually I'm somewhat inebriated and bored.
It should have been the opposite

Never mind nor time
I'm still waiting for you

[syhprum]

When I was at school I annoyed my maths teacher by insisting that the product of infinity and zero was one by cancelling the zeros in the expression 1/0 = infinity times 0/1= zero  =1/1.

[syhprum]

"And the beauty of it all is that the only thing a computer knows is binary logic" one of the famous early computers ENIAC was decimal.

[Bill S]

As usual, I’m not keeping up with threads/discussions, nor having time to catch up.  However, in the course of “weeding out” old stuff on my HD, I’ve found several things I had filed for “attention later”.   A link to this thread is one of them.

Chiral; as OP, did you get what you were looking for from the thread?  I enjoyed it, but have several points to clarify;  (one at a time, perhaps).

There is a commonly presented notion that infinite sets must contain everything.

Mathematically, this is not possible; because there is more than one infinity, so, unless every infinity contains every other infinity, no infinity contains everything. (?) 

If every infinity contained every other infinity, I think that would mean that there was only one infinity, even in maths.  That doesn’t make much sense to me.

[andreasva]

You always need a reality double check.   Monkeys live, and monkeys die, as does everything.  There can never be an infinity of monkeys, nor anything else, at any given moment in time.  You can have an infinitely rising number of monkeys over time, but infinity is not within reach for the monkeys.   They have neither the time,  nor the quantity to accomplish such a task.    Not even human beings could accomplish such ridiculous task. 

It’s a meaningless fantasy formula. 

The other argument is, random is driven by complexity.  There is no random events, just highly complex events that appear random.   Things happen for a reason.  Monkeys have no reason to type, therefore, it is impossible. 

[andreasva]

Mathematically, this is not possible; because there is more than one infinity, so, unless every infinity contains every other infinity, no infinity contains everything. (?) 

There is no such thing as infinite quantities.    Think about it. 

[Paul25]

That seems to be the case

[yor_on]

Well, a dice have no memory, right?
But I think monkeys do

[Lightraigne]

What is Shakespeare if not one of those monkey’s over time?

[Deecart]

Practicaly, you dont need to wait an infinity of time so as to have some particular finite succession of symbols.
One monkey can do it straightforward.
But with one monkey only to be sure that he has typed the right succession of symbols, you need to have waited an infinity of time.
If you have not waited an infinity of time, let say you have waited "only" some billion of billion of years, it is very unlikely that the monkey dident succeed, but it is possible that he dident succeed, so you can not claim to be sure.

You can do the same reasoning with a money coin (not a monkey money of course) and find out that it has nothing to do with the complexity of the succession of the symbols.
How long need i to wait (with let say trying one coin toss every second)  to be sure that i have at least one time Odd ?
Mathematicaly we need to have tried an infinity of time.

Furthermore, if you have an infinity of monkeys you know that an infinity of monkeys among the infinity of monkeys will write this succession of symbols straightforward. So saying you need to wait some infinity of time so as to be sure some monkey succeed is false in this case and adding the infinity of time in the scenario of an infinity of monkeys is redundant (this second requirement can be discarded)

[alancalverd]

Given that humans have evolved from monkey-like creatures in a finite time, and that there is a finite number of humans, the fact that the works of Shakespeare have already been written by one human shows that it is not merely conceivable but actually already achieved for one randomly specified document.

Therefore the evidence suggests that any specifiable document could be generated in a finite time by a finite number of animals, even though the numbers might be very large.

The problem however is that the question asks whether "everything" could be generated, to which the answer is always going to be "no" because  however many documents you have produced, you still haven't produced the catalog or index of those documents, which is itself a document that must be catalogued......

[Deecart]

The problem however is that the question asks whether "everything" could be generated, to which the answer is always going to be "no" because  however many documents you have produced, you still haven't produced the catalog or index of those documents, which is itself a document that must be catalogued......

This is effectivly a problem, because for some set of n elements you can have n! (n factorial so (n*(n-1)*(n-2)*...1) possible catalogues.
If you want to create catalogues of the catalogues you will then have (n!)! possible catalogues and so forth, so in my opinion you end up with an infinity of catalogues, even starting with a finite number of elements of the primary set.