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Topic: Infinity can not exist
Replies: 115   Last Post: Apr 9, 2010 12:08 AM

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 Kent Paul Dolan Posts: 543 Registered: 12/7/04
Re: Infinity can not exist
Posted: Jul 16, 2004 2:34 AM

"raydpratt" <raydpratt@hotmail.com> wrote:

> I recently came to understand why an infinite
> series of coin flips will never result in all
> heads or all tails even though either of such a
> series is in fact one of the possible series among
> all the infinite possibilities.

Umm. No, you still need to work on that, I think.

The reason an infinite series of coin flips wil
never result in all heads or all tails is because an
infinite series will never "result" [at least not in
the "cardinals" kind of infinity].

You can't, at least in a proof, talk about doing
something with an infinite series "at the end", or
"after it's done". There doesn't seem to _be_ an
"end". It is _never_ "done".

You cannot talk about what eventuates "after" an
infinite series. Unlike a finite series, an infinite
series isn't a product, it's a process.

The best you can do is to describe the situation
after any finite number of steps, and then describe
a situation the infinite series "approximates more
and more closely with more and more steps", if there
is any such; or describe a situation "after the next
step" if you are, say, doing a proof by induction.

Or so I understand.

Now the theory of "ordinals", which I do not
understand _at all_, works under entirely different
rules, and in particular, you _can_ stick something
onto the far end of an infinity and have that make
sense.

Just not to me. <grin>

xanthian.

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