Re: U2 Query: file locations

[David Auerbach auerbach@xxxxxxxx]

Recursion (in general) is a way of generating an infinite object from
a finite specification. Thus, we define the natural numbers as the
smallest set containing zero and the sucessor of anything in the set.
  The standard cute example writing a recursive note for the milk
deliverer for getting your milk delivered everyday: "Deliver a bottle
today and read this note tomorrow."
  Fancier recursion (but not much fancier) occur in the
definitions of standard arithmetic operations like addition:
x + 0 =x
x + (y+1) = (x+y) + 1
(explanation: we assume we have the operation of adding 1 (aka
"successor"). Now I want to calculate, according to the definition,
what 44 + 3 is. Well, 44+3 is, by the second clause above (44+2)+1. 
And by that clause, 44+2 is (44+1)+1. Substituting we have 44+3=
((44+1)+1)+1. 44+1, by that second clause, is (44+0)+1. Now first
clause to rescue, 44+0=44. Sooooo, 44+3=44+1+1+1+1.
   Of course, multiplication can be defined similarly (left as an
exercise for the reader) and various famous series (e.g., Fibonacci)
can be somewhat more complicatedly, but recursively, defined.
   It turns that what is of some interest is what *can't* be
recursively characterized.
  You can all wake up now, I'm done.

On Nov 28, at 3:24 PM, Patricia M. Godfrey wrote:
>  what's called recursion,