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heff001
- 30
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Zermelo-Fraenkel Axioms - the Axiom of Choice (ZFC), is conceptually incoherent. To me, they stole Cantor’s brilliant work and minimized it. Replies?
Higher set theory is a branch of mathematics that deals with the study of sets and their properties, specifically those that are infinite or uncountable. It extends the basic concepts of set theory to larger and more complex sets, such as those involving infinite cardinal numbers.
Cantorian sets, also known as Cantor sets, are a type of fractal set that was first described by the mathematician Georg Cantor. They are constructed by repeatedly removing the middle third of a line segment, creating a set that is uncountable and has a fractal-like structure.
Large cardinals are types of infinite cardinal numbers that are larger than the standard infinity (aleph-null). They are used in higher set theory to study the properties of very large sets and to explore the limits of what can be proven within the framework of set theory.
Large cardinals and Cantorian sets are both concepts that arise in higher set theory. Cantorian sets are used to construct large cardinals, and large cardinals are often used to prove the existence of certain types of Cantorian sets. They are both essential tools in the study of infinite sets and their properties.
The study of higher set theory is important because it allows us to understand and explore the properties of infinite sets, which have many applications in mathematics and other fields. It also helps us to better understand the limits of what can be proven within the framework of set theory and to develop new mathematical tools and techniques for dealing with infinite sets.