Chris Angelico writes: > On Wed, Feb 12, 2014 at 7:17 PM, Ben Finney wrote: > > What specific behaviour would, for you, qualify as “works with the > > set of real numbers in any way”? > > Being able to represent surds, pi, e, etc, for a start. It'd > theoretically be possible with an algebraic notation (eg by carrying > through some representation like "2*pi" rather than 6.28....), but > otherwise, irrationals can't be represented with finite storage and > a digit-based system.
I've seen papers on exact computable reals that would, in effect, generate more precision when needed for some operation. It wasn't symbolic like 2pi, more like 6.28... with a promise to delve into the ellipsis, and some notable operations not supported. Equality testing was missing, I think, and I think it could not be known in general whether such a number is positive, zero or negative, so even approximate printing in the usual digit notation would not be possible. (Interval arithmetic, I hear, has a similar problem about not knowing the sign of a number.) In stark contrast, exact rationals work nicely, up to efficiency considerations. -- https://mail.python.org/mailman/listinfo/python-list
