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- Author: Paul Halmos
- Title: Naive Set Theory
- Amazon Link: https://www.amazon.com/dp/1614271313/?tag=pfamazon01-20
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I guess one downside is that it doesn't develop set theory using ZFC IIRC.jmjlt88 said:There are really no downsides to this text. Like I mentioned earlier, I used this book as a light supplement.
Warning: when he says you will never resurface, he isn't kidding.jmjlt88 said:For those interested diving deep into Set Theory (and perhaps never surfacing), Jech's tome would certainly be one route to take. =)
Naive Set Theory is a branch of mathematical logic that deals with the study of sets, which are collections of objects or elements. It was developed by mathematician Paul Halmos and is based on the idea of intuitively defining sets rather than using formal axioms.
The basic concepts of Naive Set Theory include sets, elements, subsets, unions, intersections, and complements. Sets are collections of objects, elements are the individual objects within a set, subsets are smaller collections of elements within a set, and unions, intersections, and complements are operations that can be performed on sets.
The main principles of Naive Set Theory include the extensionality principle, which states that two sets are equal if and only if they have the same elements, and the comprehension principle, which states that a set can be defined by specifying the properties that its elements must satisfy.
One of the main limitations of Naive Set Theory is that it does not have a formal and rigorous foundation, which can lead to paradoxes and inconsistencies. It also does not have the ability to handle infinite sets and cannot account for the concept of infinity itself.
Naive Set Theory forms the basis for many other areas of mathematics, such as algebra, topology, and analysis. It is also used in other fields such as computer science, philosophy, and linguistics, as it provides a powerful framework for understanding and analyzing mathematical structures and concepts.