Elementary calculus can be done without limits, though I don't see the point in trying.
And Gabriel's pretty far from accomplishing it.
See "Calculus Unlimited," by Marsden & Weinstein.
On Mon, 25 Aug 2014 17:55:52 -0600, Robert Hansen <firstname.lastname@example.org> wrote:
> > On Aug 25, 2014, at 5:13 PM, Dave L. Renfro <email@example.com> wrote: > >> First, it's not clear to me what the role of m and n are. >> Are we to take the double limit as (m,n) --> (0,0) (and if so, do we >> assume the ratio m/n is fixed during this process)? Are we to take >> an iterated limit in which we take the limit m --> 0 for fixed nonzero >> values of n and then follow-up with a limit as n --> 0 (or reverse >> the order)? > > I feel enough shame as it is for posting the link. > > 1. I am certain he doesn?t intend for us to take a limit of any kind > because that is the whole point of inventing a new calculus without > limits. > > 2. He seems to be saying (in the PDFs) that since Q(m.n), which is all > the factors including m and n after you apply his asymmetrical > difference quotient, must equal zero when the secant and tangent have > the same slope, that we can go ahead and just ignore them. In other > words, m and n don?t matter. > > For example, using the difference quotient we are familiar with, well, I > am familiar with (you are obviously familiar with many more)? > > For f = x^2 > > delta-y/delta-x = ((x+h)^2 - x^2) / h > > = (x^2 + 2xh + h^2 - x^2) / h > > = 2x + h > > h = 0 > > f?(x) = 2x > > See, no limits.:) > > Bob Hansen
- -- - --Louis A. Talman Department of Mathematical and Computer Sciences Metropolitan State University of Denver