# Vladimir_Nesov comments on Book Review: Naive Set Theory (MIRI research guide)

• When I first worked through this book, it didn’t result in long-term retention of the material (I’m sure some people will be able to manage, just not me, not without meditating on it much longer than it takes to work through or setting up a spaced repetition system). In that respect, Enderton’s Elements of Set Theory worked much better. Enderton’s book goes into more detail, giving enough time to exercise intuition about standard proofs. At the same time, it’s an easier read, which might be helpful if Halmos’s text seems difficult.

• In general, reading about the same subject from a different author is a great way to learn and retain the material better. This is true even if neither author is objectively “better” than the other. Something about recognizing the same underlying concept expressed in different words helps to fix that concept in the mind.

It’s possible to exploit this phenomenon even when you have only one text to work with. One trick I use when working through a math text is to willfully use different notation in my notes next to the text. Using a different notation forces me to make sure that I’m really following the details of the argument. Expressing the same logic in different symbols makes it easier to see through those symbols to the underlying logic.

• The author of the Teach Yourself Logic study guide agrees with you about reading multiple sources:

I very strongly recommend tackling an area of logic (or indeed any new area of mathematics) by reading a series of books which overlap in level (with the next one covering some of the same ground and then pushing on from the previous one), rather than trying to proceed by big leaps.

In fact, I probably can’t stress this advice too much, which is why I am highlighting it here. For this approach will really help to reinforce and deepen understanding as you re-encounter the same material from different angles, with different emphases.

• Thanks for the tip. Two other books on the subject that seem to be appreciated are Introduction to Set Theory by Karel Hrbacek and Classic Set Theory: For Guided Independent Study by Derek Goldrei.

Edit: math.se weighs in: http://​​math.stackexchange.com/​​a/​​264277/​​255573