Re: Calculus XOR Probability

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

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