I've just read Chapter 7 of Alice in Numberland by Baylis and Haggarty, it's called "Nests - in which the rationals give birth to the reals and the scene is set for arithmetic in $\mathbb{R}$". Unfortunately, I could follow barely any of this chapter - I've tried to find an introduction to nests online but I can't really find anything. Does anyone know a good resource for this?
Thank you.
Sounds like a fun book, but I'm unfamiliar with it. Any sincere imitation of Lewis Carroll (Rev. Charles L. Dodson) would entail some word play.
Here I suspect "nests" is used as proxy for nets, a way of approaching convergence that's more general than limits of sequences.
Sequences are good enough for convergence in metric topological spaces, but one topic where we are spoonfed a little of the more general approach is when we tackle integration. Refinement of partitions for Riemann integrals is an example of using nets to approximate, rather than sequences.