I agree "we
should think of Infinity as a set of values itself rather than a single
value, that is, something representing many possible values from which
no particular value can be determined."
My wording on my vote was imprecise.
"Infinity" may mean the mathematical concept which as Scott
says is not a single value, or it may mean the bit pattern which is a single
value of a variable or expession and which represents the concept which
is an infinite set of infinite values. In IEEE 754 it also represents
an infinite set of finite overflow values, greater than the maximum representable
finite value but less than infinity. In my job the second meaning
is more common. Generally the context makes it clear, but in this
case it did not. I apologize for any confusion and thank Scott for
the clarification.
- Ian McIntosh
Toronto IBM Lab 8200 Warden D2-445
----- Forwarded by Ian
McIntosh/Toronto/IBM on 20/04/2009 08:17 PM -----
Scott Ferson <scott@xxxxxxxxx>
20/04/2009 07:27 PM
Please respond to
Scott Ferson <scott@xxxxxxxxx>
To
Ian McIntosh/Toronto/IBM@IBMCA
cc
Subject
Motion P1788/M003.01_Set_of_reals NO
NO
I have two problems with the definitions. An interval should be an
abstraction. A set of reals is one possible incarnation, but so is
a set a probability distributions all of whose supports are constrained
by the endpoints. It doesn't seem like good mathematics to be unnecessarily
specific.
I agree with most of Ian Macintosh's views, except to say that, from the
perspective of non-standard analysis, it seems that we should think of
Infinity as a set of values itself rather than a single value, that is,
something representing many possible values from which no particular value
can be determinied. This goes for infinitesimals too, such as 1/Infinity,
which are useful in defining open and partially open intervals.