>not using this god tier book
>introduction to proof
>>7656887
what's so funny you bumfucker
>>7657434
Not to comment on the contents of a book I've never read, but you should have been introduced to proof at the high school level, not at the upper division level.
>>7657434
In Eurabia we prove shit in high school without some book telling us how to do it step by step.
>>7656428
I like this book. It covers the same material as Spivak but it's more formal and rigorous. It starts off describing formal logic and then gives an axiomatization of the real numbers (Spivak only briefly mentions Dedekind cuts in his appendix and refers people to Landau's Foundations of Analysis book, also an excellent book). There are a few mistakes in a few of the proofs and it does end very early (does not cover multivariable).
It's similar enough to Spivak that you could use Spivak as a reference though I often found it necessary to work the other way around until I just flat out moved on to Lay's Analysis.
>>7657809
>But that's nothing like in this book at all. In the first part of this book you learn proving injectivity/surjectivity, simple topology proofs, cardinality, sequences, etc.
But you'll learn that in every Analysis book, that's how maths is taught - with proofs.
Any Analysis book that needs to explicitly mention this is most probably shit-tier.
Also: Baby Rudin is the only book.
>>7658016
>Dedekind cuts
I just read the wiki page.
Fucking hell you autists are retarded.
Why do you need superfluous shit like this?
I'm so happy I went applied master race.
> It covers the same material as Spivak but it's more formal and rigorous.
In what sense is it more formal and rigorous? A truly formal and rigorous presentation would be one done in a programming language like Automath, Coq or HOL/Isabelle. Everything else is informal.
>>7658045
>superfluous
I don't think you know what that word means.
>>7658045
>Applied
>Glorified engineer
> Why do you need superfluous shit like this?
> I'm so happy I went applied master race.
Your kind doesn't even need real numbers. Enjoy your finite-precision floating point numbers.
>>7658059
Pretty sure you need to be working in intuitionistic logic in order to invoke the Curry-Howard correspondence there boss.
any analysis book that doesn't cover sheaf cohomology isn't even a real book
>>7658028
>Also: Baby Rudin is the only book.
You misspelled Royden, but it's okay.
> Pretty sure you need to be working in intuitionistic logic in order to invoke the Curry-Howard correspondence there boss.
That makes no sense. Curry-Howard has nothing to do with the logic being used. Also, you can do classical logic in any of the programming languages I mentioned.
Why are math aspies so obsessed with real analysis texts?
By the way, Royden has zero examples. This can be either a good thing (if you like thinking hard) or a bad thing (if you need examples to build up intuition).
>>7658080
I read an introductory analysis text once that didn't cover descent theory. Into the trash it went.
>>7658097
because mathematicians can't even write a good one because analysis is such a trash tier subject, so there's a lot to nitpick.
fucking shit real analysis i fucking hated that class
complex analysis is so much better
>>7658134
Buttmad because you failed analysis?
>>7658156
no, it's just an uninspired subject.
>>7658134
Except K&F isn't an introduction to analysis. It's on basic functional analysis and measure.
>>7657809
I proved shit like Fermat's little theorem, the formulas for derivatives, several sum formulas, the cardinality of a power set etc. And this was considered basic stuff.
>>7658134
Is there really not a single good Real Analysis book?
>>7658087
Seriously, Rudin is overrated garbage intended for audience without access to many other resources in analysis as its publication was in the 1950s. The problems are great but the exposition is just complete shit.
>>7658045
you must be a freshman or something? even if you're applied you should have heard of dedekind cuts if you're around math at all
>>7659368
johnsonbaugh and pfaffenberger - foundations of mathematical analysis
>>7660258
overrateed yes, garbage no
is there some sort of compiled list to download all these books?
>>7662347
yes, check /t/ (torrent board in 4chan).
there is a torrent file with 10 GB of Maths books
>>7658064
>Applied
>Engineer whos bad at physics
Fixed that for you
