Elements of Set Theory

by Herbert B. Enderton

This is an introductory undergraduate textbook in set theory. In mathematics these days, essentially everything is a set. Some knowledge of set theory is necessary part of the background everyone needs for further study of mathematics. It is also possible to study set theory for its own interest--it is a subject with intruiging results anout simple objects. This book starts with material that nobody can do without. There is no end to what can be learned of set theory, but here is a beginning.

Genres: Mathematics, Logic, Nonfiction, Textbooks, Education, Philosophy, Science

296 pages, Hardcover

First published April 28, 1977

Reviews

[Liu · Rating 5 out of 5]

I definitely recommend this book to anyone that would like to self-study Set Theory.

This is a quite good book introducing Set Theory. It's a bit more than "Naive Set Theory" by Paul R. Halmos, while not so deep as discussing proofs and forcing.

I was reading "Set Theory" by Thomas Jech at the beginning, and found that it's too difficult for me. Jech lists quite a lot results and some are merely showing up in exercises. That's necessary, for a compact book covering widely spread topics. However the mathematician's mind is a bit too much for me to follow.

Enderton's style is what I like, that is, he explains "why" mathematicians do it like this. A good example is the Recursion Theorem. Thomas just lists it out, leaving me quite lost staring at the couple of lines. Enderton explains from an instinct point of view first, then explains to generalize it, and also to rewording through the "class" concept, there have to be some change. I suddenly grasped the idea!

Enderton also introduces different options of the setup. For example, in real number construction, he explains there are 3 ways, by decimal extension, by Cauch series, or, as he adopted, by Dedekind's cut.

For those would like to try a bit more deep topics, the last two chapters are a good start. Especially the last one, where Enderton introduced 3 topics where interested readers could carry on.

I'm happy to find Enderton's composition, finally I could lay back comfortably assuring myself that I do understand the Set Theory a bit now, not too much, not too many challenging stuffs, but the basic clearly explained and concepts concretely constructed.

If time permits, I'll re-read the last two chapters again and do some exercises.

[Carter · Rating 3 out of 5]

This book is a fairly good introduction, but for me, it is a bit too basic. I have seen most of the topics elsewhere. There are some details that I haven't seen, and perhaps the perspective is also a bit different.

[Anthony O'Connor · Rating 3 out of 5]

This one is not so good.
Covers the basics OK but then seems to go off the deep end in the final couple of chapters.
Becoming more or less unreadable.
The author did the same thing in his text on mathematical logic.
Or maybe its just me. I don't know.

[Ahmed Khaled]

A great detailed textbook

[Simon Eatwell · Rating 5 out of 5]

Archaic are some notations.

[Neelima]

Read

[3P · Rating 4 out of 5]

Good book for straightening out your thought processes.

Bad for learning transfinite induction.

[Sasha · Rating 5 out of 5]

Funniest math book out there. It can make you laugh and it can make you cry all in one sitting. Highly recommend.

[Ling Wang · Rating 4 out of 5]

看到2/3就看不太下去了，由此更加敬畏数学家，他们是几个字母加数字就能玩一辈子的家伙，orz。
虽然最后两章放弃了，但我确认对于真得能够静下心来读完的人来说，这肯定是一本好书。

[Saman · Rating 2 out of 5]

Not a bad book but it's nothing special , the ordinary theorem lemma proof book.

[Lulu]

Set theory and logic

[Teressa]

Seems like something that will come in handy for future exploration of mathematics.