Development
The hyperreals can be developed either axiomatically or by more constructively oriented methods. The essence of the axiomatic approach is to assert (1) the existence of at least one infinitesimal number, and (2) the validity of the transfer principle. In the following subsection we give a detailed outline of a more constructive approach. This method allows one to construct the hyperreals if given a set-theoretic object called an ultrafilter, but the ultrafilter itself cannot be explicitly constructed. (Kanovei and Shelah have found a method that gives an explicit construction, at the cost of a significantly more complicated treatment.)
Read more about this topic: Hyperreal Number
Famous quotes containing the word development:
“Understanding child development takes the emphasis away from the child’s character—looking at the child as good or bad. The emphasis is put on behavior as communication. Discipline is thus seen as problem-solving. The child is helped to learn a more acceptable manner of communication.”
—Ellen Galinsky (20th century)
“I’ve always been impressed by the different paths babies take in their physical development on the way to walking. It’s rare to see a behavior that starts out with such wide natural variation, yet becomes so uniform after only a few months.”
—Lawrence Kutner (20th century)
“As long as fathers rule but do not nurture, as long as mothers nurture but do not rule, the conditions favoring the development of father-daughter incest will prevail.”
—Judith Lewis Herman (b. 1942)