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.
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.