Set theory is a branch of mathematical logic that studies sets, which informally are collections of objects

**S****et theory: **

Sets, subsets, operations with sets:

union,intersection, difference, symmetric difference,

Cartesian product and disjoint union.

Functions: graph of a function.

Composition; injections,

surjections, bijections, inverse function.

**Computing cardinals: **

Cardinality of Cartesian product, union.

Cardinality of all functions from a set to another set.

Cardinality of all injective, surjective

bijective functions from a set to another set.

Infinite sets, finite sets.

Countable sets,

properties, examples (Z, Q).

R is not countable. R, RxR, RxRxR have the same cardinal.

Operations with cardinal numbers.

Cantor-Bernstein theorem.

**Relations: **

Equivalence relations,

partitions, quotient set; examples,

parallelism, similarity of triangles.

Order relations, min, max, inf, sup; linear order.

Examples: N, Z, R, *P*(*A*). Well ordered sets and induction.

Inductively ordered sets and Zorn’s lemma.

**M****athematical logic:**

Propositional Calculus.

Truth tables. Predicate Calculus.

- Advances in Mathematics ResearchAlbert R. Baswell

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Nova Science Publishers, Inc.

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CRC Press

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John Wiley & Sons, Incorporated

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Mathematical Association of America

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Elsevier Science

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OUP Oxford

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John Wiley & Sons, Incorporated

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