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

Well,I asked about Binomial Theorem as I could not understand it.I was reading about it in a chapter concerning the number system.

That second part of the inquiry makes all the diffeence in the world.  My reaction must have appeared too intense, but, well, you see, I had read that only about 10% of "professional programmers" today could, out of the blue, with just editor and debugger, write a binary search program in C++ from sratch, with the proper #includes on the fly.  The dependence upon libraries, while good (and compicated) for PRODUCTION, may not be that good for Lifelong Learning and deepening of understanding.

Your approach is your own, and for whatever energies were diverted from rigid technical education, you have invested in literature and philosophy and just trying to BE YOU.

I only wished to display how one might see the code as poetry.   That was that, and now THIS is this.

Sorry if I am so particular, but I am intent on leaving the other thread for showing how to explore such code with gdb debugger.

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When you mentioned the binomial theorem,  my mind went back to code for Combinations which I wished to include in a customized major tweaking and alteration of a calculator project from the Stroustrup text.  The nCk [read "n choose k"] can actually represent each coefficient in the polynomial expansion of (a + b)^n

The Binomial Theorem is just a series of observations about the exact nature of this expansion.

Please understand that, when it comes to mathematics I may sound like a robot, but I assure you this is where the poetry hides, in the rigor, seriousness, and clarity of thought.

I was also tempted by the free-flowing AntiOedipus Schizoanalysis, and I can certainly see where your Lovercraftian tastes would be drawn to the oozing manifold of mulitplicities.

I, on the other hand, may have sold my soul to the Devil for the pure delight in algebraic structures, and the manipulations of such structures.

Forgive my rigor and my tendency to have more respect for high school level topics than the obfusificated tomes worshipped by critical theorists.   On the other hand, I also sympathize strongly with those repelled by the rigor of mathematical proofs.

I am in between, not quite with Artuad, no - and again no - certainly not trying to stand in any shadows of Kant, Knuth, nor Stroustrup.   I think my perspective might be valuable to YOU in particular, Holden.

My recent encounter with the nature of these expansions of (a + b)^n involved defining the factorial 0! = 1, 1! = 1, 2! = 1 * 2, etc...

The numbers get very big so the challenge for me was to use special libraries [GMP] for doing the Combinations (n choose k), which involve factorials ... the Binomial Theorem - that series of observations - are tied up in this, so it is difficult to pin it down as an object in the phenomenal world.  I am not being purposely obtuse in trying to extract a more detailed inquiry from you, Holden.

Anything having to do with our number systems can be intensely fascinating.   I was inspired to write some code about representing decimal fractions, with repeating decimals, non-terminating or terminating decimals.

The numbers to the right of the decimal point are a series, a sum of a sequence of decimal fractions in places 1/10, 1/100, 1/1000, ...

If we can narrow down where you are confused, whether about the nature of number systems in general, or where the expansions of (a + b)^n come into play, I would be able to assist in a more helpful manner.   The last thing I want to do is discourage you asking me a question or dampen your taste for such things.

I will eat Steel Cut Oats and keep an eye on this thread over the coming weeks.
In the meantime, I might also use that little site for some temporary links for our exploration of exactly where your interest and confusion is.

Keep in mind that my back aches from strain, and that I am no academic.  I trust that you respect my life as a lifelong Learner.  I have documumented my own explorations, and I will offer you this kind of support now or for however long we are able.  This way we might zero in on some topics for you to return to later when, say, one of us is preoccupied with the an engagement with their Lord or Destroyer (Grim Reaper).

Perspective:  Mass Pandemic Hysteria?  All we can do is groan.  Without health, these words do not exist.   The world is our idea.  Without health, the cosmos vanishes.