Suppose each of an infinite number of possible somethings happens
without result on an infinite number of occasions, and each occasion
takes zero time. After some time one of the somethings happens with a
result.

Do we have an uncountable but finite number of occasions?

Help?

a not-very-good mathematician

Peter Fairbrother

Peter Fairbrother explained :
> Suppose each of an infinite number of possible somethings happens without
> result on an infinite number of occasions, and each occasion takes zero time.
> After some time one of the somethings happens with a result.
>
> Do we have an uncountable but finite number of occasions?
>
> Help?

No, and yes. You have to start with a premise which is true in order to
have any idea of the truth value of a consequence. From a falsehood,
anything is possible.

On 24/08/2023 22:58, FromTheRafters wrote:
> Peter Fairbrother explained :
>> Suppose each of an infinite number of possible somethings happens
>> without result on an infinite number of occasions, and each occasion
>> takes zero time. After some time one of the somethings happens with a
>> result.
>>
>> Do we have an uncountable but finite number of occasions?
>>
>> Help?
>
> No, and yes. You have to start with a premise which is true in order to
> have any idea of the truth value of a consequence. From a falsehood,
> anything is possible.

Are you saying that my supposition is somehow false? Impossible?

If not, where is the falsehood?

Peter F

On 25/08/2023 01:11, FromTheRafters wrote:
> Peter Fairbrother presented the following explanation :
>> On 24/08/2023 22:58, FromTheRafters wrote:
>>> Peter Fairbrother explained :
>>>> Suppose each of an infinite number of possible somethings happens
>>>> without result on an infinite number of occasions, and each occasion
>>>> takes zero time. After some time one of the somethings happens with
>>>> a result.
>>>>
>>>> Do we have an uncountable but finite number of occasions?
>>>>
>>>> Help?
>>>
>>> No, and yes. You have to start with a premise which is true in order
>>> to have any idea of the truth value of a consequence. From a
>>> falsehood, anything is possible.
>>
>> Are you saying that my supposition is somehow false? Impossible?
>
> As I read it, a 'real' probability exists that something (an event) will
> or will not happen in so many tries (occasions). With (countably?)
> infinitely many tries, it is a non-zero probability that it does happen
> unless it can never happen. You then suppose that after some infinitely
> many tries, that it does indeed happen.
>
> Then, you throw in time as zero for the event and then say that some
> time passes and you do get a result. Time is irrelevant here isn't it?
> You simply force a result by words here. If it cannot happen, you cannot
> make it happen just by saying it happens.

And yet it moves. ;)

This is about quantum collapse in an alternative interpretation of
Feynman's sum-over-paths interpretation of quantum mechanics.

The somethings are paths taken without result - so, how many paths are
taken? I suppose infinite possible different paths, and infinite numbers
of each path, in zero time. So far, so good.

But after some time - I'm reminded of Xeno - one of the paths becomes
"real".

> Yes, your countably infinitely many tries and your uncountably
> infinitely many real number non-zero probability event figures seem to
> have you at odds with sizes of infinite sets.

yep.

:)

Peter F

the real good stuff is yet to come...

On 25/08/2023 03:33, Peter Fairbrother wrote:
> On 25/08/2023 01:11, FromTheRafters wrote:

>> Yes, your countably infinitely many tries and your uncountably
>> infinitely many real number non-zero probability event figures seem to
>> have you at odds with sizes of infinite sets.

Or to make it simpler, how do mathematicians handle a selection from an
infinite set?

I don't think probability theory comes in there?

Peter F

On 8/24/2023 2:45 PM, Peter Fairbrother wrote:
> Suppose each of an infinite number of possible somethings happens
> without result on an infinite number of occasions, and each occasion
> takes zero time. After some time one of the somethings happens with a
> result.
>
> Do we have an uncountable but finite number of occasions?
>
> Help?
>
>
> a not-very-good mathematician
>

Imagine creating a number from a 10-ary die. You roll the die, get a
number from 0...9, write it down. So, you start:

i[0] = 1
i[1] = 7
i[2] = 9
i[3] = 5
i[4] = 1
i[5] = 2
....

So, we can say:

i[0...5] = .179512

It goes on and on. Afaict, this is an infinite number... Yet finite at
every stage of iteration,, basically, every roll... Every digit is
determined by a random 10-ary die roll. It might be irrational as
well... :^)

Peter Fairbrother <peter@tsto.co.uk> writes:
> Suppose each of an infinite number

You're going to have to define what you mean by "number" such that you
can have "an infinite number". Your question is presented in the human
language of English, not the formal language of mathematics, and the
simplest English interpretation of "number" (typically aligning with
what the mathematician would call the Natural Numbers) does not admit
any "infinite numbers".

Phil
--
We are no longer hunters and nomads. No longer awed and frightened, as we have
gained some understanding of the world in which we live. As such, we can cast
aside childish remnants from the dawn of our civilization.
-- NotSanguine on SoylentNews, after Eugen Weber in /The Western Tradition/