Introduction to nests

Question

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.

Is it perhaps a play on words, "nests" as a pun on "nets" and the approach to convergence? — hardmath, Jul 03 '14 at 10:34

score 1 · Accepted Answer · answered Jul 03 '14 at 11:53

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.

Introduction to nests

1 Answers1