RE: Re: Re: Question about Replace

*To*: mathgroup at smc.vnet.net*Subject*: [mg35791] RE: [mg35761] Re: [mg35753] Re: Question about Replace*From*: "DrBob" <majort at cox-internet.com>*Date*: Wed, 31 Jul 2002 01:33:31 -0400 (EDT)*Reply-to*: <drbob at bigfoot.com>*Sender*: owner-wri-mathgroup at wolfram.com

I agree. I had a graduate math course in non-standard analysis years ago, and I recall that it was just as formally logical as the usual way. Integrals became "finite" (transfinite) sums and the usual proofs of calculus became much simpler, once the groundwork was laid. It could be tricky to incorporate it in Mathematica, but no more so than intervals or complex numbers. The synthesis of integration with summation could be very powerful, too, as each can build on the other. Ditto for differentiation and finite differences, differential equations and difference equations, etc. Bobby Treat -----Original Message----- From: Andrzej Kozlowski [mailto:andrzej at tuins.ac.jp] To: mathgroup at smc.vnet.net Subject: [mg35791] [mg35761] Re: [mg35753] Re: Question about Replace While Berkeley's critique of 18th century Calculus was right at the time, Abraham Robinson showed that ultimately that the intuition behind the sort of thing that Leibnitz and others did was right and could be completely formalized and turned into a very powerful tool. It certainly would be nice to implement non-standard analysis in Mathematica (perhaps someone has already done this?). Indeed one can in this way turn calculus into algebra (getting rid of the concept of Limit) and it may well be the most natural approach to calculus via symbolic algebra. (For more see Abraham Robinson, "Non-standard Analysis", Princeton Landmarks in Mathematics, 1996). Andrzej Kozlowski Toyama International University JAPAN http://platon.c.u-tokyo.ac.jp/andrzej/ On Monday, July 29, 2002, at 04:13 PM, John Doty wrote: > In article <ai06os$1f6$1 at smc.vnet.net>, "Andrzej Kozlowski" > <andrzej at tuins.ac.jp> wrote: > >> Actually on second thoughts I began to suspect that this question is >> related to another one posted by Heather, concerning simplifying >> expressions in which x is "much larger than" y. I am not at all sure if >> a sensible calculus of this kind can be developed but obviously >> Simplify >> will not do this. > > It seems to me that this is essentially a (capital-C) "Calculus" > problem, > and unless a simple /.y->0 is what's wanted, the correct tool is > Limit[]. > Berkeley's critique of 18th century Calculus applies here: while it was > essentially antiscientific, his reasoning was flawless and should warn > us > against trying to solve this sort of problem by mindless algebra. > > Of course, Limit[] is a tricky and somewhat unreliable power tool, > requiring caution. This reflects the mathematical subtlety of this kind > of problem. It is generally essential to formulate the problem in such a > way that the direction of the approach to the limit is unambiguous. > > -- > | John Doty "You can't confuse me, that's my job." > | Home: jpd at w-d.org > | Work: jpd at space.mit.edu > > >

**RE: Animation looping glitch (confirmed)**

**More weird integration issues...**

**Re: RE: RE: Question about Replace**

**Installing package "SpreadOption`"**