We begin BookofProofs with a branch of mathematics dedicated to the set theory.
Set theory is the systematic study of principles governing sets, which are the most basic mathematical objects. The four basics even a non-mathematician has to know about sets are:
- Sets can be completely described (defined) by either listing all their elements or defining the properties, the elements must fulfill.
- An object belongs to a set, if it is listed in the set or if it fulfills the defined properties.
- Sets do not allow duplicates (taking an element out of the set removes this element from the set completely).
- If you remove every element from the set, it becomes empty, (but it still exists, like it was an “empty container”).
Theoretical minimum (in a nutshell)
The study of set theory is highly intuitive and accessible to the undergraduates. However, understanding of the meaning of Zermelo-Fraenkel Axioms might be somewhat demanding at the beginning. It’s definitely worth the effort!
Concepts you will learn in this part of BookofProofs
- What are the Zermelo-Fraenkel Axioms and how to define sets using them?
- Which are the set operations and how to “calculate” with sets?
- How can sets be “compared with each other” and start a fascinating journey into infinite sets using ordinals?
- How can sets be used to “count things” and learn even more astonishing things about infinite sets, called cardinals?
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