Re: infinity

Tony Orlow (aeo6) <aeo6@xxxxxxxxxxx> wrote:
Tony Orlow (aeo6) <aeo6@xxxxxxxxxxx> wrote:
> stephen@xxxxxxxxxx said:
>> Just as there is no step where the number of balls becomes
>> infinite but at the end the number of balls is infinite.
>>
>> Do you agree with that or not? Is there a step at which
>> the number of balls becomes infinite? Is there
>> some finite n such that n+9 is infinite? You heartily
>> deny this everytime it is brought up, but now you
>> are implying that there is some step at which the balls
>> become infinite.
> The balls, like the natural numbers, become infinite after an infinite number
> of steps. All steps before noon are finite, but AT noon, the rate of iteration
> becomes infinite, and all infinite steps occur then. An infinite number of
> finite steps, or a finite number of infinite steps, is necessary to reach
> infinity.

You still have not identified the step at which they become
infinite. 'After an infinite number of steps' is not very
precise, and does not describe how you get from a finite
number to an infinite number. There either is a step
that starts with a finite number of balls and ends with
an infinite number of balls, or there is not a step that
starts with a finite number of balls and ends with an infinite
number of balls. You seem reluctant to actually state
whether you believe such a step exists. If the step
does not exist, you cannot get there, according to your logic.


By the way, how many steps are there before noon? Why
does it require an infinite number of steps to use
up all the finite numbers if there are only a finite number
of them?


<snip>


>> > Um, is it, or is it not possible to get zero by subtracting 1 from 1? Is it
>> > possible to empty the vase by removing a ball at a time, and not have a last
>> > ball? This is absurdity in perfect form.
>>
>> Is it possible to get an infinite number of balls by adding
>> a finite number of balls to a finite number of balls? At
>> every step we start with a finite number of balls, and add
>> a finite number of balls.
> If you do it an infinite number of times, then you cannot avoid having an
> infinite sum.

You are still talking about something that does not happen.
There is no such step. Why would doing something infinitely
many times make the nonexistent step suddenly happen?
Why does it not cause the nonexistent step of there
being 0 balls to happen?

>>
>> Why is it necessary that there is a step that results in
>> zero balls but it is not necessary that there is a step
>> that results in an infinite number of balls?
> You are removing the balls one at a time and claiming the vase empties, that's
> why.

And you are adding balls a finite quantity at a time and claiming
that the quantity becomes infinite. So in order to get an infinite
number, there must be a step where n was finite, and then n+9 was
infinite. That is your logic. You still have not explained
why you get to have results that are not produced by any
step, but noone else is.

>>
>> You also agree that if we start with an infinite number
>> of balls and remove them 1 at a time at the specified times
>> we end up with zero balls. What is the last ball removed
>> in that case?
> Depends what the last ball in was. According to the problem schedule, as I've
> said, yor infinity would be log2(N), where N is the number of moments ina
> minute.

My infinity is the endless sort. Not your weird version
of infinity that ends. There is no ball labelled N or
log2(N).

In any case, assuming time is continuous, there are far more
moments in a minute than there are natural numbers.

>>
>> When you use the word 'possible' I wonder if you are
>> somehow imagining that this scenario is physically possible.
> Don't be stupid.

So what do you mean by 'possible'?

>> It is clearly physically impossible. You cannot move
>> balls arbirtarily fast, and there is apparently not enough
>> matter in the universe to create an infinite number
>> of ping pong balls. So what do you mean by 'possible'?
>> The whole situation is physically impossible. Mathematical
>> possibility and physical possiblity are not the same thing.
> Yeah, so it should seem obvious that I mean mathematically possible, in the
> context of the whole of math.

But it is clearly mathematically possible. Every ball
is removed before noon. For every ball labelled n that is added
before noon, that ball is removed before noon. Simple.
In the 10 in, 1 out, ball n is added at time noon-(1/2)^(ceiling(n/10))
and removed at time noon-(1/2)^n. For all finite n,
both of those quantities are before noon. Even if we allow
your infinite numbers, they are all added and removed at
exactly noon, and spend exactly no time in the vase and
so are never in the vase. It is mathematically impossible
for any ball to be in the vase at noon, unless you believe
in some number n such that (1/2)^(ceiling(n/10))>=0 and
(1/2)^n<0.

I thought of one last example to try to explain infinity
to you. First off you have to recognize when I say 'endless'
I truly mean without end. I do not mean that there is really
an end out there that I just have not specified. You seem
incapable of imagining 'endless' and always insist on putting
an end on things, but just try to imagine something that
truly does not end.

So for the duration of this post, lets call a set infinite
if it does not have a last element. Consider the set
S = { { 1 },
{ 1, 2 },
{ 1, 2, 3 },
{ 1, 2, 3, 4 },
{ 1, 2, 3, 4, 5 },
etc.

This set has no last element. It just keeps going.
There is no end. It is infinite.

Each element S however is a finite set.
Each element of S is a set of the form {1 , .... n }.
Each element of S begins with 1, and ends with some n.
Each element has an end, and is therefore finite.

Now I guess you will disagree with this. Either
you will claim that S has a last element, which if you
do you need to identify what it is, or you will
claim that one of the elements of S does not have
a last element. Again you will have to identify
which of the elements of S does not have a last element.

Stephen














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