Re: infinity

Tony Orlow (aeo6) <aeo6@xxxxxxxxxxx> writes:

> Jesse F. Hughes said:
>> Tony Orlow (aeo6) <aeo6@xxxxxxxxxxx> writes:
>>
>> > Jesse F. Hughes said:
>> >> Tony Orlow (aeo6) <aeo6@xxxxxxxxxxx> writes:
>> >>
>> >> > Virgil said:
>> >> >> In article <MPG.1d618aae41392f57989fe9@xxxxxxxxxxxxxxxxxxxxxxxxx>,
>> >> >> Tony Orlow (aeo6) <aeo6@xxxxxxxxxxx> wrote:
>> >> >>
>> >> >> > > Which ball is not covered by that argument?
>> >> >> > N+1 through 10n+9.
>> >> >>
>> >> >> If TO means "n+1 through 10n+9" he is presuming that there is a last,
>> >> >> nth, step, which is specifically prohibited by the rules.
>> >> >>
>> >> >> And as there is no last step, there is no ball that is not covered.
>> >> >>
>> >> > Then there is no point at which the last ball is removed. Isn't that
>> >> > correct?
>> >>
>> >> The last ball? What's the number written on that one? When was it
>> >> put in?
>> > "largest finite. largest finite."
>>
>> Let's call this largest finite number x.
> I was referring to the fact that you always try to turn it into a
> matter of whether there is a largest finite or not, even when that
> is irrelevant, and try to assert that I am claiming there is a
> largest finite, despite repeated asserions on my part to the
> contrary. Talk about stupid.

I did misunderstand you, then. But you're utterly wrong when you
claim I was trying to talk about the "largest finite number". Nothing
I said was directed that way.

I simply ask: when *you* refer to the last ball removed, which ball
*is* that?


>> Now, by definition of the problem, every ball labeled n is put in at
>> time
>>
>> noon - 2^(-f(n))
>>
>> where f(n) = floor(n / 10). Right?
> Wrong. Iteration n occurs at time noon - minute * 1/2^n. What are you applying
> your floor() function to? Minutes? That would make every iteration happen at
> 11:59.

No. The first ten balls (which I label 0 - 9, for convenience) are
put in at 11:59. The next ten at 11:59:30, the next at 11:59:45 and
so on.

You are misreading my function. "n" is the label of a ball and ball n
goes in at noon - 2^(floor (n/10))


>> So ball x was put in at
>> noon - 2^(-f(x)). This is before noon, so 2^(-f(x)) must be greater
>> than zero, right?

> Not at n=oo, unless you allow for infinitesimals.

None of the balls are labeled oo, so that's utterly irrelevant. By
assumption, each ball is labeled with some natural number. oo is not a
natural number.


[...]

>> Now, I'd think that this is also before noon, but apparently you don't
>> think so. Thus, it appears that we have deduced a startling property
>> of the largest finite number:
>>
>> 2^(-floor(x/10)) > 0, but 2^(-x) <= 0.
>>
>> Wow. I wonder whether 2^(-floor(x/2)) > 0 or not.
>>
>> How did you ever deduce this startling fact?
> I don't know. You just did that, and it decayed from the beginning into
> senseless drivel, starting with the very first mistake.

I thought you were serious about the largest finite natural number.
Since you weren't, these comments don't apply.

> At any finite amount of time before noon, n is finite, obviously. All the
> infinite iterations happen AT noon, since they take INFINITESIMAL amounts of
> time. That is where your infinite set comes from, at that very last moment.
> That moment does not include an emptying of the vase.
>
> Every time you remove a ball, you have just added 10. There is no
> way you ever reduce the number to zero. This is logic. What you are
> doing is obfuscation.

Oh. *This* is logic. Goodness me.

Look, it's quite simple. Every ball put into the vase has a number on
it. Can you tell me the number of any ball that is still in the vase
at noon? If not, why not?


[...]

>> > If you claim that the vase at some point becomes empty, and want to
>> > challenge those that claim otherwise by asking which ball remains,
>> > then they have equal right to ask which is the final ball removed
>> > which leaves the vase empty.
>>
>> They have that right, but it's a stupid question. There is no such
>> thing as the final ball and the vase is non-empty for every time prior
>> to noon (after 11:59).

> But at some point all balls are removed. When is that, and how does
> it happen, without adding more balls than are removed, when you add
> ten before removing any one ball? It's not a stupid question at
> all. Certainly no more stupid than asking which ball is left. The
> fact that there is any question that there are an infinite number of
> balls in the vase at noon is stupid. Ask any school child, and you
> will get my answer. Try to explain your answer, and they will glaze
> over and eventually agree simply due to your authority, the same way
> you did when you first swallowed this junk.

But we never claim that there is a last ball removed. Since there is
no "last ball" put in, there is no contradiction when there is no last
ball removed.

On the other hand, asking which balls are left is an obvious question.
What numbers are present in the vase? Why doesn't it bother you that
you can't answer this question?

I can answer yours. There was no final ball removed. Whenever a ball
is removed, there is a later time at which another ball will be
removed, so no ball is the final ball.

And the vase becomes empty at noon and not an instant before. (It is
certainly unintuitive, but so is the hypothesis that we insert and
remove balls in ever decreasing intervals, going to 0 in the limit.)

[...]

>> This is related to your belief that there is a
>> largest natural number.

> I have repeatedly stated that I have no such belief. Your repetition
> of this lie only demonstrates your inability to listen and remember
> anything except what was already implanted in the fungal region of
> your brain.


I misunderstood your initial comment.

[...]

--
"Mathematicians are rather important in the infrastructures of many
organizations that protect civilization. I've determined that they
are a consistent security risk, and seem to have other agendas, other
loyalties beyond loyalty to their respective nations." -- James Harris
.

Relevant Pages

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