numbers.rb

class Zero
  def pred
    self
  end

  def succ
    Number.new(self)
  end

  def +(other)
    other
  end

  def to_s
    ""
  end

  def inspect
    "Zero"
  end
end

class Number
  attr_reader :pred

  def initialize(pred = NotANumber.new)
    @pred = pred
  end

  def succ
    Number.new(self)
  end

  def +(other)
    Number.new(pred + Number.new(other.pred))
  end

  def to_s
    "." + @pred.to_s
  end

  def inspect
    "<Number #{to_s} @pred=#{@pred.inspect}>"
  end
end

irb(main):074:0> zero = Zero.new
=> Zero
irb(main):075:0> one = zero.succ
=> <Number . @pred=Zero>
irb(main):076:0> one + one
=> <Number .. @pred=<Number . @pred=Zero>>
irb(main):077:0> two = one.succ
=> <Number .. @pred=<Number . @pred=Zero>>
irb(main):078:0> two + one
=> <Number ... @pred=<Number .. @pred=<Number . @pred=Zero>>>
irb(main):079:0> two + two
=> <Number .... @pred=<Number ... @pred=<Number .. @pred=<Number . @pred=Zero>>>>
irb(main):080:0> zero + two
=> <Number .. @pred=<Number . @pred=Zero>>

Weird unnecessary complexity. There is no need to use Number.new(other.pred) in the addition as that is identical to other. The definition of plus should simply be:

  def +(other)
    Number.new(pred + other)
  end