As I've seen it used in engineering it means different from zero by some small but non-vanishing amount. It is bigger than infinitesimal, which is a value that goes to zero in some limit. The "finite" value doesn't go to zero. It's used in contrast to "infinitesimal", not "infinite". Brent On 9/4/2016 5:04 PM, Bill Gosper wrote:
Your car's gearbox has the finite gears and neutral. For accelerating, neutral = 0. For engine breaking and roll starting, neutral = ∞.
On 2016-09-04 09:11, Tomas Rokicki wrote:
It's an interesting use of the word "finite" in the sense that the opposite of "finite" probably needs to be "infinite", but here the opposite appears to be "zero". Further, if we are looking at a case like this, a "small but non-zero" asymptote implies a satisfying population for "finite" would have to be, in count, *infinite*.
I believe we are in the world of Humpty Dumpty here.
On Sun, Sep 4, 2016 at 5:54 AM, Veit Elser <ve10@cornell.edu> wrote:
I raised this point in a Physics Today letter to the editor (1980s) and was met with unanimous defense of this usage of “finite”.
-Veit Physicists take logarithms a lot. --rwg
On Sep 3, 2016, at 9:45 PM, James Propp <jamespropp@gmail.com> wrote:
Are you using "finite" to mean "nonzero", Bill?
I have always disparaged this usage, but maybe I should reconsider my prejudice. What do you all think about this?
Jim Propp
On Saturday, September 3, 2016, Bill Gosper <billgosper@gmail.com <javascript:_e(%7B%7D,'cvml','billgosper@gmail.com');>> wrote:
Despite my distaste for decimal digits, I noticed ... Is the asymptotic density finite? --rwg
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