Infinite Ranges in Ruby (cont.)

When I wrote yesterday that Ruby ranges may be infinite the first example that came to my mind as I was writing the mail in ruby-talk involved an enumeration of the rationals in [0, 1] and that somewhat obscured my point.

There's a more simple approach where you define <=> and succ in a class which consists of the naturals plus the first infinite ordinals ω, ω + 1, ω + 2, ... In that class 1 .. ω is an infinite range. But I didn't want to present this alternate proof because albeit I could skip set theory jargon altogether, using numbers past infinity was conceptually not a big gain over the previous reasoning.

Late at night I finally was able to construct an analogous argument to the one that uses ordinals, but just using Z × Z, which can be thought as a set of pairs of integers by any programmer and so it was much more understandable in the mailing list. This is the resulting class:

      class ZSquared
        include Comparable
    
        attr_reader :n, :m
    
        def initialize(n, m)
          @n, @m = n, m
        end
    
        def succ
          self.class.new(n+1, m)
        end
      
        def <=>(zs)
          [self.m, self.n] <=> [zs.m, zs.n]
        end
      end

which allows the definition of an infinite Range:

      ZSquared.new(0, 0) .. ZSquared.new(0, 1)

So yes, Ruby ranges may be infinite, and thus Range#length defined as a loop over succ wouldn't necessarily terminate.