... encoding function intermediate value theorem binary tree Cantor set fundamental theorem of algebra Gauss proof of FTA Heine Borel theorem Simpson Stephen fallen leaf tree infinite uniform continuity classical proof extreme value theorem Riemann integral ACA0 Riemann mapping theorem...

... for a comparison of the results obtained in it with those obtained within classical reverse mathematics as well as to prove theorems in Bishop's constructive mathematics. The chapter also formalizes results on compactness properties, such as the Heine-Borel theorem, the Cantor intersection theorem, the Bolzano...

...This chapter explores the basic concepts that arise when real numbers and continuous functions are studied, particularly the limit concept and its use in proving properties of continuous functions. It gives proofs of the Bolzano–Weierstrass and Heine–Borel theorems, and the intermediate and extreme...