My 254th book of science Curiosity of sequences and progressions at infinity borderline 1*10^604 and its algebraic completeness 1*10^1208
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Archimedes Plutonium<plutonium.archimedes@gmail.com>
Jul 21, 2023, 3:44:32 AM
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My 254th book of science

Curiosity of sequences and progressions at infinity borderline 1*10^604 and its algebraic completeness 1*10^1208

I need to write a book on a list of curiosity progressions and how they fare once they reach the infinity borderline.

Recently this year I asked Dan Joyce what the Primitive Pythagorean Triples nearest the infinity borderline were like, thinking they had some special feature. The borderline is where pi has 3 zero digits in a row for the first time.

But tonight I have a new fascinating curiosity of a progression.

Notice that the encasement of progressive cubes. Something I mentioned yesterday in my 250th book TEACHING TRUE CHEMISTRY.

So we start this progression or sequence with 1. Now we ask how many unit blocks cubes are need to enclose completely that 1 block? And the answer is a 3 by 3 by 3 = 3^3 = 27 unit blocks to enclose the 1 block. Now we ask how many unit blocks to enclose
the 27 block? And the answer is we add 2 to 3 = 5, so that a 5^3 block completely encloses the 27 block. We go to the next enclosement of 5+2 = 7 and thus 7^3 encloses the 5^3.

Now that is all straightforward.

However there is a bizarre surprise in this sequence once we divide.

Our sequence is 1, 27, 125, 343, 729, 1331,....

So we divide former into next one starting at 27. 125/27, 343/125, 729/343, 1331/729, . . .

4.62... , 2.74..., 2.12..., 1.82..., ....

So, well that is rather bizarre that it is shrinking which the mind would think should be getting larger and unbounded.

So the question here is, at infinity borderline, what is the number that this converges to????

Also include even numbers. 2^3, 4^3, 6^3, 8^3, ...

So this book is about the piling up of questions about what happens at the infinity borderline and its algebraic completeness.

AP, King of Science
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Archimedes Plutonium
Jul 21, 2023, 3:26:34 PM
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On Friday, July 21, 2023 at 2:58:32 PM UTC-5, Archimedes Plutonium wrote in sci.math: > But let me
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Archimedes Plutonium
Jul 22, 2023, 4:57:56 PM
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On Friday, July 21, 2023 Archimedes Plutonium wrote in sci.math: So this is a new idea in math
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Archimedes Plutonium
Jul 23, 2023, 3:01:28 AM
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Archimedes Plutonium 2:18 AM 23Jul2023    to So now this is my 254th book of science to be
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Archimedes Plutonium
Jul 23, 2023, 1:49:18 PM
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I am going to have to rewrite Polynomials graphing. Using Stewart, Redlin, Watson, 4ed, College
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Archimedes Plutonium
Jul 23, 2023, 2:03:14 PM
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AP's 254th book of science // Massive Overhaul of Sequence theory and Polynomial Graphing in Old
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Archimedes Plutonium
Jul 23, 2023, 10:36:56 PM
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So here, one of the greatest failings of Old Math is never a decent lecture on Equation or equality,
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Archimedes Plutonium
Jul 23, 2023, 10:57:18 PM
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So in Old Math, when they graphed polynomials, they brought everything over on to the leftside of
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Archimedes Plutonium
Jul 24, 2023, 9:35:01 AM
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254th book Massive Overhaul of Sequence theory and Polynomial Graphing Alright, well, now I am
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Archimedes Plutonium
Jul 24, 2023, 11:13:54 AM
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AP's 254th book of science // Massive Overhaul of Sequence theory and Polynomial Graphing in Old
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Archimedes Plutonium
Jul 24, 2023, 11:41:59 AM
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On Monday, July 24, 2023 at 11:13:11 AM UTC-5, Archimedes Plutonium wrote: > AP's 254th book
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Archimedes Plutonium
Jul 24, 2023, 6:45:10 PM
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The pain in writing this book, is to join it all together, for I am all over the map on this. I will
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Archimedes Plutonium
Jul 25, 2023, 1:06:11 AM
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The nasty habit in Old Math on polynomial graphing, make the y-axis uneven with x-axis. I was looking
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Archimedes Plutonium
Jul 25, 2023, 3:00:37 AM
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Alright, the 5x^2 looked so much like a length of the circle arc, that I had to investigate it
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Archimedes Plutonium
Jul 25, 2023, 3:50:31 AM
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On Tuesday, July 25, 2023 at 3:00:03 AM UTC-5, Archimedes Plutonium wrote: > Alright, the 5x^2
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Archimedes Plutonium
Jul 25, 2023, 1:42:50 PM
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On Tuesday, July 25, 2023 at 3:49:58 AM UTC-5, Archimedes Plutonium wrote: > On Tuesday, July 25,
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Archimedes Plutonium
Jul 26, 2023, 2:01:10 AM
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In this overhaul, the graphing of Polynomials of Old Math is all screwed up. For in the graphing
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Archimedes Plutonium
Jul 26, 2023, 4:21:29 AM
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Alright, a problem I have been storaging for a long time, but no appropriate environment to present
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Archimedes Plutonium
Jul 26, 2023, 1:29:18 PM
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Alright, looks like I will be able to sharpen up the definition of Function. In the past I was
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Archimedes Plutonium
Jul 26, 2023, 2:29:56 PM
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Now the sequence as a function shows best why step functions are bogus, and phony baloney. Because a
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Archimedes Plutonium
Jul 26, 2023, 3:01:48 PM
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The big take away lesson of today-- a function of mathematics has to engulf the entire x-axis. It
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Archimedes Plutonium
Jul 26, 2023, 4:16:28 PM
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Now I am looking for a method of covering every function in a Decimal Grid System with a polynomial.
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Archimedes Plutonium
Jul 26, 2023, 4:44:19 PM
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For a sawtooth polynomial function, I am going to need something like a remake of the sine or cosine.
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Archimedes Plutonium
Jul 26, 2023, 5:10:30 PM
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Alright, I found the solution. I seldom like being in a state of vexation. The solution involves
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Archimedes Plutonium
Jul 26, 2023, 5:34:28 PM
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So, well, I added something spectacularly new to Calculus, the most important math subject there is.
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Archimedes Plutonium
Aug 20, 2023, 7:39:57 PM (yesterday)
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Yes, my 254th book
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Archimedes Plutonium<plutonium.archimedes@gmail.com>
1:09 AM (now)
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So far my title is

Overhauling Math Sequence & Series theory

Why an overhaul? Because the only valid functions of math are polynomial functions and this impacts what is a Sequence and what is a Series.

AP

AP's 254th book of science// Overhauling Math Sequence & Series theory

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