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Re:A Software Engineer’s Adventures in Learning Mathematics by Pyret on Wednesday February 04, 2015 @09:13AM (#8996843)
Well, there is no shortage of very good and VERY SIMPLE and rigorous intros to analysis books out today:

How to Think About Analysis by Lara Alcock.

Understanding Analysis by Stephen Abbot.

Mathematical Analysis and Proof by David Stirling.

Numbers and Functions: Steps into Analysis by Burn.

Analysis: With an Introduction to Proof by Steven Lay.

A First Course in Mathematical Analysis by David Brannan.

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