[Axiom-developer] [RealNumbers] real references

[wyscc]

Changes http://page.axiom-developer.org/zope/mathaction/RealNumbers/diff
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>From wyscc Wed Jun 15 01:36:00 -4:00<br>

Bill, thanks for creating this page. I enjoyed reading the links and was 
wondering how a site on labor laws need to know the foundations of mathematics. 
Actually, they gave credit to the following (open) source::

http://en.wikipedia.org/wiki/Real_number<br>
http://en.wikipedia.org/wiki/Computable_number

It is interesting to note that order relations are not computable and that sums 
of digit-enumerable real numbers are in general not digit-enumerable. This 
reminds me that when I teach power series solution to differential equations, I 
use the analog of decimal numbers and comment that power series are easier, 
because they involve no carry. The same reason shows the infinite sequence 
approach to infinite precision floating point (essentially using 
digit-enumeration Turing machines) discussed in #167 Infinite Floats Domain 
will not work. IPFP is different from power series!

Wikipedia also has an introduction to floating point systems::

http://en.wikipedia.org/wiki/Floating_point

For in depth study, I recommend the book::

Pat H. Sterbenz, Floating-Point Computation, Prentice Hall, 1974.

Sterbenz worked at IBM Systems Research Institute, New York at the time of 
writing the book.

William

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