Set theory - OKN2310N08
Title: Teorie množin
Guaranteed by: Katedra matematiky a didaktiky matematiky (41-KMDM)
Faculty: Faculty of Education
Actual: from 2019
Semester: winter
E-Credits: 1
Examination process: winter s.:oral
Hours per week, examination: winter s.:0/0, MC [HS]
Extent per academic year: 4 [hours]
Capacity: unknown / unknown (50)
Min. number of students: unlimited
4EU+: no
Virtual mobility / capacity: no
State of the course: not taught
Language: Czech
Teaching methods: combined
Note: course can be enrolled in outside the study plan
enabled for web enrollment
priority enrollment if the course is part of the study plan
Guarantor: prof. RNDr. Ladislav Kvasz, DSc., Dr.
Interchangeability : OKN2310008
Is co-requisite for: OKN1310101
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Annotation -
Basic notions of set theory. Cardinality of a set, countable and uncountable sets. Cardinal and ordinal numbers, Zermelo's axiom of choice and its consequences. Cantor's discontinuum and its properties. Peano's curve.
Last update: JANCARIK/PEDF.CUNI.CZ (27.06.2012)
Aim of the course -

The aim of the course is a refinement of the notion of infinity by means of Cantorian set theory. Examples from arithmetic and geometry which offer a deeper insight into the notion of infinity (such as Cantor's discontinuum, Peano's curve) will be presented.

Last update: JANCARIK/PEDF.CUNI.CZ (27.06.2012)
Literature -
Alexandrov, P. S.: Úvod do teorie množin a funkcí

Sierpinski, W.: Cardinal and ordinal numbers

Balcar, B.- Štěpánek, P.: Teorie množin

Bukovský, L.: Množiny a všeličo okolo nich

Rohlíčková, I.: Aritmetika konečných a nekonečných množin

Bečvář, J.a kol.: Seznamujeme se s množinami

Pospíšil, B.: Nekonečno v matematice

Vilenkin, N. J.: Nekonečné množiny

Last update: JANCARIK/PEDF.CUNI.CZ (27.06.2012)
Teaching methods -

Lecture and seminar.

Last update: JANCARIK/PEDF.CUNI.CZ (27.06.2012)
Syllabus -
  • Comparison of sets. Equivalence of sets.
  • Finite and infinite sets.
  • The principle of exclusion and inclusion for finite sets.
  • Comparison of the cardinality of a given set with its power set.
  • countable and uncountable sets.
  • The uncountability of the set of all real numbers.
  • Cantor's discontinuum and its properties.
  • The equivalence of Cantor's discontinuum and the set of all real numbers.
  • The equivalence of a line segment with a cube.
  • Cardinal numbers, the sum, product and power of cardinal numbers.
  • Zermelo's axiom of choice and Zermelo's theorem on well ordering.
Last update: JANCARIK/PEDF.CUNI.CZ (27.06.2012)