2.15.3 Decimal Expansions

A real number is represented by an infinite, base b, decimal expansion :

With a ``floating'' decimal place and a sign indicator, every real number has a representation. Some numbers, such as , may be expanded into a finite decimal expansion. An example with b=10 is:

which also shows that such numbers have two infinite forms. Only the second form, with the infinite tail of ``0'' digits, is to be used. With this convention, every real number has a unique representation.

Operations are defined as operations on the infinite sums corresponding to the real numbers' decimal expansions. Addition is a simple example:

After rearranging the expression so that one term corresponds to each digit ``carrying'' must take place to ensure .

This representation introduces difficulties and is not commonly used as a formal definition of real numbers. See [10] for further details concerning this representation and associated methods.

Jeff Tupper

March 1996