Instead he asked for my email address. The next morning the following email message awaited me. Dear Gary, It was fun to have a chat at Ihor's party. This morning I got out my all time favorite source of information on things worthwhile, the Ninth Edition of the Encyclopedia Britannica. It is very clear.
Fractions come about by dividing unity into parts, and are thus by definition positive.
In the past, you might hope that he forgot the matter. Today, Billy can post his discovery on the Internet and engage in serious conversation - perhaps even research with other mathematicians. Access to computers and software environments like MicroWorlds makes it possible for children to make discoveries that may be of interest to mathematicians and scientists. It is plausible that kids can contribute to the construction of knowledge deemed important by adults.