If anyone else got curious about induction on the reals, my first interesting result was this Math.StackExchange post: <a href="http:&#x2F;&#x2F;math.stackexchange.com&#x2F;questions&#x2F;4202&#x2F;induction-on-real-numbers" rel="nofollow">http:&#x2F;&#x2F;math.stackexchange.com&#x2F;questions&#x2F;4202&#x2F;induction-on-re...</a>