{∅, {∅}, {∅, {∅}}} : Rage Against the Meat Grinder

I am glad we have this thread separate from the one where I list all the various textbooks in the "mysterious" Dolciani series for I have tracked down and received a most unique edition of an Algerba textbook which, by section 2-7, covers precisely what I was finding so "unfamiliar" in the Introductory Analysis text I mentioned.

I am not suggesting you search for this book as I have noticed it can be quite expensive.  I happened to get lucky so I pounced on it.

For future reference:  Student edition Algebra 1 c 1985 or 1988 or 2006 by Dolciani, Swanson, and Graham

The teacher's edition (which is more suited for self-study, I think) at Amazon is the correct ISBN, and the authors name + page numbers are listed wrong.  What I did was to contact seller and verify that this was in fact by Dolciani/Swanson/Graham c 1985 and not "Totten, Douglas Smith" (misprint).


Those specific authors (Dolciani/Swanson/Graham) are important, for there are other editions (Dolciani/Brown/Cole) which make no mention whatsoever of the particular topic of interest, that is, proving theorems using the field axioms of real numbers.

I am so relieved to that the book exists.  You see, Holden, it is not any of the algebraic methods that I feel are weird.  It is this way of writing formal proofs with the axoims and properties of the real numbers.   None of this is covered in any courses I took in college, and I suspect that, for math majors, they might expect one to already be familiar with this.  So, I was able to track this rare source down that presents the material for beginners.  It's a rare thing.  From what I have researched, this may be the only such book to attempt to teach it at the beginner's level.

My idea is to scan certain pages and email them to you when I settle down.  This way you can decide for yourself whether such material qualifies as "the Weird".

I am rushing out to visit my father in the hospital.  Internal complications.  I am not sure about details.

Before going, I wanted to post here in case I am involved in some vehicular misadventure.  At least I will die knowing I passed on this clue to you as far as where to look for just what I have been trying to become more familiar with.  A teacher's edition has solutions.  That is the copy I found for less than what the student's edition goes for.  Maybe I have invisible allies?

Over the summer, I would like to introduce you to the material to see if you have ever seen such formal proofs at the level of basic field axioms.   For some reason, it all seems so strange to have to prove that -(-a) = a, and to use the fact that 0 = (-a + a) in order to prove it.

Got to go.    Stay safe!