Infinity may or may not be a number, depending on your
definitions of a number. (I think most mathematicians are still
using Frege's definition, by which a number is "the set of all
sets equivalent to a given set." Using that definition, infinity
is as valid a number as 3.) It's been a long time since I worked
with any of this stuff, but there are at least two approaches to infinity.
One is the cardinal number (size of a set) one, which gives us
aleph-null, aleph-one, the Cantorian diagonal argument,
and the like. The other is via ordinal numbers, where the first
infinite ordinal--defined as the smallest number larger than
all the finite integers--is called epsilon-zero. (That should be
a Greek lower-case epsilon with the subscript 0, but I can't
do that in ASCII.)
Neither is merely "a number so large that it cannot be written
easily." 300 to the ten trillionth power is larger than most of us
can imagine, but it can be written quickly and easily--and is
larger than we're likely to have any use for. It is also finite.
Doing arithmetic with infinity is tricky. So are the assumptions
here. For starters, what does it mean to say that the probability
of a given event happening at a particular point in space-time
is 1/oo? How is that different from the probability being zero?
Secondly, in what sense is time "probably infinite"?
If you're arguing that it can be chopped into arbitrarily small
pieces, that's both unproven--has anyone even undertaken to
determine whether time is quantized--and possibly irrelevant,
since the event may need at least x amount of time to happen
in. And the universe may not be open-ended: I'm a bit
suspicious of the "balanced universe" arguments, since they
seem to be largely a matter of aesthetically based wishful
thinking, but that by itself doesn't mean that the universe _isn't_
closed.
Vicki
rosenzweig@acm.org
----------
From: owner-virus
To: virus
Subject: Re: virus: Real World?
Date: Monday, January 06, 1997 3:30PM
David McFadzean wrote:
> > From: jonesr@gatwick.geco-prakla.slb.com
> > Date: Tuesday, December 31, 1996 2:59 AM
>
> > Here's a little theory that one of my friends invented whilst extremely
> drunk:
> >
> > If the probability of any event occurring at any time and at any point
in
> > space is 1/oo (where oo = infinity), and given that time is /probably/
> infinite,
> > irrespective of the state of the universe, then there are an infinite
> number of
> > instances at which an event can occur. Hence, the probability of any
> event
> > happening in the Universe, or one before it, or one after it, is denoted
> as:
> > 1/oo * oo = 1/1 Therefore, the event must occur.
>
> You're friend must have been extremely drunk.
Yup, he's a medical student :)
> By the same reasoning, if
> I flip a coin twice the chances of getting tails is 100% (1/2 * 2 = 1/1).
Not true, but if you flip a coin an infinite amount of times, you will get
tails an infinite amount of times. You will also get heads an infinite
amount of times - I think ;P
> Besides, doing arithmetic with infinities is risky business;
True, I hate infinities equations, esp. WRT to graphs.
> you have to
> be sure they are of the same order (aleph null, etc.) and some operations
> (like addition) don't make sense (oo + 1 = oo).
Yep, but it must be remembered that oo is not a number, it is a
representation
of a number so huge that it cannot be written easily. Therefore, the above
equation /is/ true.
Drakir
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Richard Jones "We are the New Breed
jonesr@gatwick.geco-prakla.slb.com We are the Future."
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