Bøger af Karel Hrbacek

This text presents an intuitive treatment of mathematics using ultrasmall numbers. With this modern approach to infinitesimals, proofs become simpler and more focused on the combinatorial heart of arguments, unlike traditional treatments that use epsilon-delta methods. Readers can fully prove fundamental results, such as the Extreme Value Theore

This text presents an intuitive treatment of mathematics using ultrasmall numbers. With this modern approach to infinitesimals, proofs become simpler and more focused on the combinatorial heart of arguments, unlike traditional treatments that use epsilon¿delta methods. Readers can fully prove fundamental results, such as the Extreme Value Theorem, from the axioms immediately, without needing to master notions of supremum or compactness. The book includes numerous exercises throughout and at the end of each chapter.

A text for mathematics courses that covers the basics such as relations, functions, orderings, finite, countable, and uncountable sets, and cardinal and ordinal numbers. It includes material on normal forms and Goodstein sequences. It provides important ideas including filters, ultrafilters, closed unbounded and stationary sets, and partitions.