
Re: Brainstorming about STEM (was About Functions)
Posted:
Dec 23, 2011 1:12 AM


> At 08:26 PM 12/17/2011, Dan Christensen wrote: > > >Do your "garden variety mathematical theories" > include things like > >number theory, abstract algebra and geometry? While > designed as > >primarily a learning aid, I see no reason that DC > Proof could not be > >used to generate most if not all of current > mathematical theory  > >that is, theories based on some underlying set, e.g. > the set of > >natural numbers in number theory, or the set of > points in a plane for geometry. > > > >Download my DC Proof 2.0 freeware at > http://www.dcproof.com > > I took a chance on infecting my computer and > downloaded your program > but I must be missing something. I couldn't see how > to make it prove > anything at all or even to verify a proof in, say, > plane > geometry.
The axioms for geometry and real numbers are not built into the DC Proof system. The numbers of axioms alone would overwhelm the beginner. For the axioms of geometry, see the work of Tarski or Hilbert. You can find a version of the axioms for the real numbers in the DC Proof/Samples directory.
Beware, though. In my experience, even elementary results in the Euclidean plane can quickly explode into proofs of several hundred, even thousands of lines. So, I really can't recommend geometry for the beginner just learning how to write mathematical proofs. Better to stick to logic, set theory, and elementary number theory, the axioms of which ARE built into DC Proof. (See "To the Educator" at my homepage.)
Dan Download my DC Proof software at http://www.dcproof.com Also see "The Barber Paradox Video."

