Re: Calculus XOR Probability

In article <MPG.1eadc4e1cc196b0298ac38@xxxxxxxxxxxxxxxxxxxxxxxxx>,
Tony Orlow <aeo6@xxxxxxxxxxx> wrote:

imaginatorium@xxxxxxxxxxxxx said:

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.

The rules above are about distinguishing the finite from the
infinite, once the concept of numbers is established.

Where does TO get his version of the reals? The rest of us start with
the naturals, and work our way up to them gradually, so that by the time
WE get them we can prove they work as expected. But TO seems to want to
do his construction from the top down.
.

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