Re: Calculus XOR Probability

In article <MPG.1eadc6b84b9328e298ac3a@xxxxxxxxxxxxxxxxxxxxxxxxx>,
Tony Orlow <aeo6@xxxxxxxxxxx> wrote:

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.

Since TO ignores the cardinal number and ordinal numbers, both of which
are well established in standard mathematics, no wonder he has to invent
something to take their place.

Unfortunately for him, TO is a very sloppy inventor, and his
replacements do not work anywhere nearly as well as what he is trying,
vainly, to replace.
.

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