Re: infinity


aeo6 Tony Orlow wrote:
> Randy Poe said:

> > Do you think the sum 1+2+3+... over the finite numbers is
> > a finite value, say F?
> sum(x=1->k:x)=(k^2+k)/2, which is finite for any finite k. Do you think there
> is a finite k s.t. (k^2+k)/2 is infinite?

Nope. Your turn. Do you think there's a finite value of k
such that sum(x=1->k:x) represents a sum of all the natural
numbers?

What value of k is that, if so?

> > There is no ooth.
> Do you have an infinite number of them or not?

Yes, one for each natural number. As you must know by now,
I and virtually everyone else in this world who's ever
taken a college-level math course understands that there are
an infinite number of natural numbers, and none of them
has the value "oo".

> Are there not balls with an an
> infinite number of predecessors?

There are not.

> When you have an infinite number of balls,
> what do the labels look like?

Each one of them looks like a finite natural number,
with a finite number of digits and a ball next to it
with a higher number, also finite.

> > There are an infinite number of words. You have said yourself
> > that the process of adding one letter to a finite word,
> > to make another finite word, never ends.
> Sure, it never ends, and if it goes on forever, then you have elongated your
> words forever

Oops. Got confused between the sets and the elements again.

No, you have no elongated any particular word, either
forever or by a single character. Every time you add a
character, your last (shorter) word is still there and you
have a new word, which is also finite.

The process of getting a new finite word goes on forever.

I can never stop getting a new finite word.

You also did your think of agreeing a process has no end and
then talking about what happens at the end. I haven't
"elongated any word forever" at the end of my infinite
process because there is no end to the infinite process.

- Randy

.

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