Robert Seeberger wrote:
----- Original Message -----
From: "Julia Thompson" <[EMAIL PROTECTED]>
To: "Killer Bs Discussion" <[email protected]>
Sent: Friday, September 29, 2006 5:34 PM
Subject: Re: Infinities large and small (was Re: The Assumption Re:
9/11conspiracies)
Nick Arnett wrote:
On 9/28/06, Ronn!Blankenship <[EMAIL PROTECTED]>
wrote:
Isn't "a little infinite" a contradiction, like "a little bit . .
. "?
No... some infinities are smaller than others, as is easily
demonstrated.
There are an infinite number of even numbers and an infinite number
of odd
numbers. Those two infinities are the same size. However, there
are an
infinite number of even AND odd numbers and that infinity is twice
as big as
the first two.
No, it's the SAME SIZE as each of the first two. THAT'S the one
that took me a week or two to wrap my head around. :)
Heh.....that depends on which mathematician you talk to. The Dedekind
Infinite is not the only view floating around.
It seems to me that this is an attempt to give infinity the same
standing as zero.
frex: 1/2 times zero = zero is equivalent to saying 1/2 times infinity
= infinity.
And that is roughly like saying 1/zero = infinity and that is a pretty
neat bit of mathematical philosophy. But for me the concept breaks
down when considered with practicality in mind. I find the statement
1/infinity = infinity to be nonsensical since one is infinitely small
and the other infinitely large and for me the implication is that all
non-zero values = infinity and that is profoundly untrue.
I would propose that 1/infinity is "approaching zero" or "roughly
equivalent to" zero, but never exactly zero.
Infinity as a value has little value.<G>
I can hold out my hand and say I have zero apples in it or I could
have one apple to show you. Zero has almost the same quantifiability
as any natural number, but the same cannot be said for infinity.
Infinity has never been shown to exist in nature. (And all the physics
in the world cannot produce infinite anything since the entire
universe would be overwhelmed by any introduction of the infinite into
the universe.)
Infinity is simply a concept, and like other concepts is malleable and
subject to fads.
I was just addressing 1) the number of even numbers, 2) the number of
odd numbers, and 3) the number of integers. There are all sorts of
infinities that are not equal to each other; but the three infinities I
list above are.
When you start talking about the reals, that's a whole bigger infinity. :)
Julia
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