I just finished writing an article whose title and content
were motivated by the discussion in this thread, so it may
be appropriate to announce it here. The article is called
"Floating point numbers are real numbers"
and it is available at:
http://arxiv.org/abs/1605.09202
I believe this title is self evident for many
members of this list, who find that it is a good idea
to have a Level 1 based on the abstract real numbers,
as in the standards we discuss here.
I also believe that Lee Winter underestimates
the value of having a great theory, as the
one for real numbers, as a foundation
on which the other Levels of our standards are
based upon.
In mathematics, a dog may have n legs and
we can use induction in n to prove results
about real dogs with four legs, whether Lincoln
would care about it or not (he was busy
building a nation...)
In fact, in many regards, it is irrelevant whether
there is a real machine which is able to compute
with abstract real numbers. What matters is whether
this machine works as expected on the finite subset
of numbers with which it is prepared to handle,
and the purpose of the other Levels of the standards
discussed here is to say what we expect from
these finite machines. However, thanks god,
Level 1 is based on real numbers.
walter.