Re: Calculus XOR Probability


Tony Orlow wrote:
imaginatorium@xxxxxxxxxxxxx said:
<snip>

Actually, I DID define all finite reals in terms of a few non-circular rules:

1) 0<x<=1 -> finite(x)
2) finite(x) -> finite(0-x)
3) finite(x) -> finite(1/x)
4) finite(x) -> finite(2^x) (optional)

Infinite values are then defined as being larger than any finite value, in
absolute terms. So, it's not really circular, but not fully finished. I'm not
sure I am comfortable that this part is complete. Sorry. I'm considering a
number of things involved in this. Suggestions? Comments?

Yes. READ A BOOK. If you had the first clue how real mathematics is
done, you might have a chance of representing what ideas you have in an
understandable way. In particular the rules above simply assume that
all the "numbers" you want are already there, and you merely say things
about how they relate to each other.

If we base your 1-4 above on normal notions of real numbers, then you
appear more or less to be describing properties such as that the
non-zero reals form a group under multiplication. The only (genuine)
real x not having your property finite(x) is zero, which you have
forgotten to define as Tinfinite; you then assume that "larger than all
of these" defines something. If you were a bit more careful, I think
you might manage to define the reals + Infinity, where x/0 = Infinity
for any nonzero real x. (The arithmetic that javascript does
beautifully, meaning that you can implement a lens calculator directly,
and type "Infinity" in the subject distance box when required. Try it:
http://imaginatorium.org/stuff/cufilter.htm )

But this is certainly not _your_ "Tinfinity", because as you tell us
all the time, yours is [are] just "like a finite number" which can be
multiplied by 2 to get a different "just like a finite number", but um
not a finite number, because it's infinitely pinker than a finite
number. Well, the whole thing works just as well if I write pink or
blue, doesn't it?

Brian Chandler
http://imaginatorium.org

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