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

Thanks Holden.   I have continuously been revisiting the topics of Sequences, Series, and Limits, so I have a sustaining interest in Arithmetic Progressions and Geometric Progressions.    I can't seem to get away from them. 

You know my case.   I destroyed my pre-2015 notebooks, and over the last few years have been amassing a long series of "math notebooks."

While they initially began with Linear Algebra, Analytic Geometry, and Calculus, over the past couple of years I have been REVISITING HIGH SCHOOL MATHEMATICS with a vengeance, and so my notebooks, with notes and completed exercises (solutions, not just answers) may represent my sole contribution before my brain goes soft and I once again gravitate towards music and oblivion.

Last night I saw many "ghosts," and they were pleased with me.   These were the "ghosts" of Mary Dolciani, Frank Allen, Edwin Beckenbach, and hundreds of others who were involved with the "School Mathematics Study Group" (1958-1977).

Even though there is nothing officially being produced by me, the trail of hand-written notebooks along with an ever-growing arsenal of computer programs (written mostly in C++) directly inspired by the material of this "high school mathematics" presented in such a rigorous manner, with great attention paid to the field axioms ...

So, with this in mind, this long project of "Hentrich Revisiting High School Mathematics," we are most definitely going to have a great deal to discuss in the future.    I will have several notebooks to scan and send to you, but it all depends on which areas you are drawn to and when.

I will be revisiting Sequences, Series, and Limits this month after going over the principle of mathematical induction.

Of course, life being what it is, and with other interests (such as programming) and demands (basic living), I can't live by the calendar or the clock.

What I mean to say is that I am not floating around the rings of Saturn.  I am not in search of the "Voice of (some) God" to reveal the nature of "infinity".   It is enough for me just to see how the idea of infinity is used in understanding why some series converge, and others do not.

Of course, our communications in no way rely on our ability to find common ground in mathematical interests (nor computing interests).   I am doing time in being.   As are you and Raul and others.   I am not involved in a "project".   As the trail of notebooks and computer code gathers, it may appear to have been a great project I was engrossed in, that is not how I approach it day by day.  I must find some kind of satisfaction in the revisiting, in the return to familiar topics, each time realizing that the amount of thinking required does not decrease over time.  Sure, there is the comforting feeling of familiarity, but then there are those honest moments when I feel as though I am being introduced to concepts for the very first time (the Beginner's Mind?).

There is no guarantee that I will be able to continue in this manner, and this will certainly not last forever.  Eventually I will either lose interest or simply will not be able to concentrate.  Often this is dictated by whatever environment I find myself in.

Study while you can, and consider you periods of "lonely isolation" to be a great blessing!

Peace.