Explanation

This repository is a personal project to work through the exercises in mathematician Terry Tao's textbook "Analysis I" by translating them into Lean, a formal proof assistant. A proof assistant is software that helps you write mathematical proofs in a way that can be automatically checked for correctness—like a very strict spell-checker for mathematics.

The original project (created by Tao himself) translates the textbook into Lean but deliberately leaves the exercise problems marked as incomplete (sorrys, in Lean terminology). This fork fills in those blanks with actual solutions. The creator is working through the book at their own pace and sharing their solutions publicly in case others find them useful as a learning resource.

The book covers foundational mathematics: starting from basic axioms about natural numbers, building up through sets, integers, rational numbers, and real numbers, then moving into analysis topics like sequences, series, limits, and continuous functions. Each section of the book corresponds to a separate file in the repository, organized by chapter. The formalization tries to stay true to how Tao presents the material in the textbook while also gradually adopting conventions from Mathlib (a large existing library of formally verified mathematics in Lean), so that readers can see how to bridge between textbook-style definitions and professional-grade proof libraries.

This project is primarily useful for people learning formal mathematics or proof assistants—especially those already studying Analysis I. It's not meant for active collaboration; the creator is clear they won't be accepting contributions. The solutions branch contains the completed proofs, while the main branch stays synchronized with Tao's original upstream version.