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Set theory - ON2310N008

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.:1/0, MC [HT]
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:	full-time
Teaching methods:	full-time
Note:	course can be enrolled in outside the study plan priority enrollment if the course is part of the study plan

Guarantor:	prof. RNDr. Ladislav Kvasz, DSc., Dr.
Interchangeability :	ON2310008
Is co-requisite for:	ON1310101

Opinion survey results Examination dates Schedule Noticeboard

Annotation -

Last update: JANCARIK/PEDF.CUNI.CZ (17.05.2012)

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.

Aim of the course -

Last update: JANCARIK/PEDF.CUNI.CZ (17.05.2012)

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.

Literature -

Last update: JANCARIK/PEDF.CUNI.CZ (17.05.2012)

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

Teaching methods -

Last update: JANCARIK/PEDF.CUNI.CZ (17.05.2012)

Lecture and seminar.

Syllabus -

Last update: JANCARIK/PEDF.CUNI.CZ (17.05.2012)

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.