Re: [HM] Infinitesimals
David Reed (dreed@math.duke.edu)
Wed, 11 Nov 1998 22:40:35 -0500 (EST)
Re Newton, Leibniz and infinitesimals. Short of non-standard analysis
there is the algebraic notion of completing a ring with respect to an
ideal (as one oftent does in algebraic geometry), for example, working
modulo higher and higher powers of x. I
cannot claim to have followed Leibniz down all of his paths, but this
seems to me to be a simpler and more likely "modern" version of what he
was doing. In fact, from the materials of both Newton and Leibniz that I
have been able to study, they seem to have had the clearest picture of
infintesimals. What muddies the water is when we import into their
thinking the later notion of "function"...
David Reed