[nicklaf]

I would be very careful before unleashing a beginner on this book. It would be too easy, IMO, for the reader to end up with the wrong idea that mechanical proofs like the ones in this book are all that are needed in mathematics, since it's possible to get as far as the real numbers (or complex numbers) with so little geometric intuition. Furthermore, the real numbers are the most concrete, familiar setting to do analysis in, but it is not healthy to spend so much focus on the concrete details of the real line so early on: a student of mathematics needs variation to keep alive her or his curiosity. Pugh does an excellent job of explaining the simple geometric essence of Dedekind cuts. In principle, one might learn something about proof writing by reading the Landau book. However, it is much, much better, IMO, to defer detailed study of something so specific, until after first surveying the setting in which the results of Landau's book are used. In most real analysis books, the reader is asked to prove a few of the results covered in Landau.

Mathematics is foremost a conceptual subject rather than a mechanical one, and it is immaterial that the reader have firsthand experience that all the theorems are proven. As one learns mathematics, it soon becomes apparent that there will always be gaps in her or his knowledge, and that is therefore best to skip steps that s/he believes could be done in principle.

[DavidWanjiru]

Are you on twitter, nicklaf? You sound like someone I'd want to be following.

[nicklaf]

Negative, but I do plan to set up a sort of homepage for my research sometime in the future. When I do, I'll link to it in my HN profile.