Re: Calculus XOR Probability

Matt Gutting said:
Tony Orlow wrote:
Matt Gutting said:
Tony Orlow wrote:
Matt Gutting said:
Tony Orlow wrote:
<snip>

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,
(Matt)
How do you know that there are any infinite n in the first place?
(Tony again)
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.
But how do you know it's an integer in the first place? In other words, what
makes you so sure that there is an integer describing the size of this set?
Must sizes always be describable by a number? If so, why?

Matt

Because the size of the set is the count of the elements included in it, as far
as I'm concerned. That's why I don't accept a system where you add an infinite
number of elements and the "size" doesn't change. You don't normally have
fractional elements in a set, so this "count" has got to be integral, whether
it's finite or infinite. Of course, if you are using something like fuzzy set
theory, you may very well have set sizes which are not integral, but I don't
think that's what we're discussing, is it?

I'm not talking about fractional set sizes. I'm asking how you know that the
descriptor which describes the size of this set is a number.

Matt


Because that's what a number IS. You have a set of objects, and you ask what
the size is. How do you measure this? For finite sets, you COUNT the objects,
and the answer is a NUMBER. So, for infinite sets, you want to claim that size
is something OTHER than a number??? Pray tell, what kind of a thing IS the size
of an infinite set, if not some kind of infinite number? If it's not a number,
what is it doing in mathematics? This just seems like a silly question.

I am reminded of a theology class I took, where the professor asked what
someone would say if they were trying to convey the idea of god to someone with
no concpt. I offered that one might observe the universe, with its vastness of
space and time, and its multitude of matter and energy and their interactions,
and ask oneself where it all came from, and call that "god". Then some tofu-
brain responded with, "Why did it have to come from anywhere?? Maybe it was
just there!!" It's the same kind of question, and not one I see much point in.

Every set has a size, and every size can be expressed in terms of some kind of
number.

--
Smiles,

Tony
.