One of the areas we haven't discussed are those decimals that do not have a power of two in their denominator and those numbers that cannot be expressed as a fraction at all. Instead, we can find infinite sequences that is between. If you're loooking for a particular number you need only to look in the right spot. All the real numbers have been created previously with Dedekind's cuts. To simplify the problem, whether you're adding or multiplying, always reduce the left and right sets.
Multiplication is just as easy.
The formula for these numbers is no different, and the calculations are no more difficult. The only rule you need to know is that the empty set plus anything is still the empty set, and the empty set times anything is still the empty set. You need java to run this. The previous is better, but you don't need java for this one. Undergraduate Research Opportunities in Combinatoral Games.