On Wed, Sep 5, 2012 at 11:38 AM, Joe Niederberger <niederberger@comcast.net> wrote: > Kirby >>> Reals in the sense of >>> infinitely precise numbers have no application in computing. >>> >> > > Paul Tanner III.1415... >> And that's where things go wrong when trying to funnel everything in >> mathematics through a computer science bottleneck. So much of the >> class of all objects studied by professional mathematicians just >> cannot fit. >> > > Here's a debate. Do mathematicians actually study infinitely precise numbers, or do they merely play games in (hopefully) consistent systems whose semantics have traditionally been explained as studying such mythical objects? The games, in as much as they have been given precise rules, appear themselves to be computational games. >
That's true only if we define "compute" a certain way.
And you can speak of irrational numbers as mythical objects all you want - but do you mean to say that natural numbers are mythical objects as well? OK, but regardless of the status of these objects, precision to as high a degree as possible in the language used in denoting the objects studied is part of the game - a necessary part of it. That requirement for precision to such a degree is part of what sets mathematics apart from other academic areas.
