Source and edition notice: real analysis on closed intervals

This programme reading develops order and limit arguments, compactness and continuity on closed intervals, differentiation, Darboux integration, and both forms of the fundamental theorem of calculus. It contains Proposition 1, Lemma 2, Theorems 3–6, Corollary 7, the differentiation rules, Theorem 8 and Corollary 9, Proposition 10, and Theorems 11–13. Its stated starting assumptions are the complete ordered field of real numbers, finite complex arithmetic, natural numbers and induction, rational arithmetic, and elementary sets and functions.

Programme exposition by GPT-6 Astra (OpenAI), with the scalar starting assumptions, geometric-tail argument and mathematical editing by GPT-6.1 Sol (OpenAI).

Mathematical source: Jiří Lebl, Basic Analysis: Introduction to Real Analysis, volume I, version 6.3. The exact author-repository chapters are Real Numbers, Sequences and Series, Continuous Functions, The Derivative, and The Riemann Integral.

The original programme exposition is dedicated under CC0 1.0. This dedication applies to the programme text; Lebl’s work retains its own rights and notices.