Re: Calculus XOR Probability

imaginatorium@xxxxxxxxxxxxx said:
Tony Orlow wrote:
David R Tribble said:
Tony Orlow wrote: [on NaN]
So, it's just a placeholder for where you might have a number, but you don't
have a number, so it's NaN. Real great. What kind of math can you do on a Java
NaN?

Pretty much the same arithmetic operations you can do on Math.INFINITY
in Java. An arithmetic operation involving a NaN results in a NaN, and
similarly any operation involving an infinity operand results in either
an infinity or a NaN.

But you're not using Java floating-point arithmetic as a basis to
explain abstract mathematics, are you?

Why don't you ask Brian why he compared infinite set sizes to NaNs in Java?

Sorry, I probably just introduced extra confusion - not something
you're exactly short on, Tony.

You described counting the size of a finite set. OK. No problem.
You suggested that *in the sense of counting a finite set*, an infinite
set does not have such a "size". Also OK - no problem.

In handling numerical calculations in Javascript and other such
languages, it is possible to give a variable any of a (very) large
number of numerical values, and also the non-numerical value
represented by the atomic symbol "NaN". In just the same way one could
identify the size of any finite set as the numerical value obtained
from a counting process, and for any set that is not a finite set, use
a "placeholder" (if you like) value which is not a size (number), but
is an atomic symbol (e.g.) 'NaS' for not-a-size.

I wondered if this might help, but it doesn't look like it.

Brian Chandler
http://imaginatorium.org



Well, that sounds almost like what the standard theory does, doesn't it? And,
what I've been advocating is a more numeric approach to infinity. I see
infinity as a quantitative concept, and seek to treat it more consistently with
the rest of math, and not as some kind of magical exception to every rule. So,
thanks for the suggestion, but it's not very satisfying, because NaS seems like
Not an Answer, and answers are there to be found.

--
Smiles,

Tony
.