Re: Calculus XOR Probability

Matt Gutting said:
Tony Orlow wrote:
imaginatorium@xxxxxxxxxxxxx said:
Tony Orlow wrote:
No, I talk more about completed actual infinities, and Han speaks more about
unboundedly large but more or less finite sets with constant relationships, but
there's not a lot of difference there, really. Brian likes to say I am talking
about the "imponderably large but finite", because I am dealing with these
infinite values similarly to finite values. So, what Han and I agree on is that
considering infinities is a lot like considering the infinite case for finite
sets, ...
OK, I'll bite. What does it mean to "consider the infinite case for
finite sets"? (I'm not entirely sure I can even parse it correctly.)


Brian Chandler
http://imaginatorium.org



Basically, all I'm saying boils down to inductive proof of equality holding for
infinite n. If some relationship between measures of a set holds for all finite
cases greater than some n, then it can be considered to hold for infinite n,

How do you know that there are any infinite n in the first place?

Because there are sets with infinite numbers of elements, such as any set of
all reals in a finite interval. You cannot have half a real number in your set,
so this infinite number is integral, and therefore part of what I consider the
integers, or hyperintegers. Otherwise, infinite sets cannot have a size, which
makes the "infinite" part kind of meaningless.


Matt
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--
Smiles,

Tony
.