Lecturer(s)


Fuchs Eduard, doc. RNDr. CSc.

Course content

Problems of infinity in mathematics. Position of infinity in antiquity, in the European Middle Ages and at present time. Origin of the set theory and its influence on 20th century mathematics. Origin of the setlogical language of contemporary mathematics. Relation between intuitive and formal constructions of mathematics. Construction of natural and real numbers in the set theory. Cardinal and ordinal numbers, transfinite induction and its connection with the mathematical induction in school mathematics. Axiom of choice and its role in contemporary mathematics. Gödel's incompleteness theorem and its impact on modern science.

Learning activities and teaching methods

Monologic (reading, lecture, briefing)

Learning outcomes

The set theory has become the world of modern mathematics. Not only has it postulated the mathematical concept of infinity in modern mathematics, it has also become the basis of almost all current mathematical disciplines. At the beginning of the 20th century it, however, largely contributed to the collapse of existing notions about the ways mathematics shoud be built. Without understanding the modern development of the set theory, the modern construction of mathematics in the 20th century cannot, therefore, be understood. Gödel's results, on the other hand, fundamentally limited the strength of the formal construction of mathematics, and completely changed existing views of the strength of exact theories. Students will be acquainted with these results as well.
basic orientation in university mathematics

Prerequisites

Successful completion of the course requires understanding of the basic concepts of the explained theory, and knowledge of definitions, theorems and proofs. The aim of the exam is to test whether a student has understood the explained theory and is able to apply it.

Assessment methods and criteria

Combined exam
Basic orientation in university mathematics.

Recommended literature


Fraenkel, A. A., BarHillel, Y.:. Foundations of Set Theory, Amsterdam, 1958.

Fuchs, E.:. Teorie množin pro učitele, MU, Brno, 2003.

Tarski, A.:. Úvod do logiky a metodologie deduktivních věd, Academia, Praha, 1966.
