> I was reading Rudy Rucker's "Infinity and the Mind", > it's pretty good reading, 70's state-of-the-art. He > mentions for example that the Dedekind construction > of the real number is the post-Aristotlean (actual infinities allowed) > Eudoxus construction. Infinity or its specter was apparent > to the early theoreticians, it is still today, and then and now > is by definition an unbounded playground of the imagination.
You'll probably find this paper pretty much explains the issues in question quite imaginatively! g!
"In "The Nature and Meaning of Numbers," Dedekind produces an original, quite remarkable proof for the holy grail in the foundations of elementary arithmetic, that there are an infinite number of things. It goes like this. [p, 64 in the Dover edition.] Consider the set S of things which can be objects of my thought. Define the function phi(s), which maps an element s of S to the thought that s can be an object of my thought. Then phi is evidently one-to-one, and the image of phi is contained in S. Indeed, it is properly contained in S, because I myself can be an object of my thoughts and so belong to S, but I myself am not a mere thought. Thus S is infinite."
peace is of the pi, d8>D At what point on the circle, does a regular, infinity-gon, inscribed inside the circle, have its inside angles equal to 179.999... degrees?