Remarks made by kimko_379

picture is from Sigeki Noya: „Mugen-Ron no Kyooshitsu = The Classroom (for Seminars) on The Infinity-Theory“ (Tokyo: Kodansha Co. Inc., 1998) with Copyright: Sigeki Noya, 1998.

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Remarks made by kimko_379

picture is from Sigeki Noya: „Mugen-Ron no Kyooshitsu = The Classroom (for Seminars) on The Infinity-Theory“ (Tokyo: Kodansha Co. Inc., 1998) with Copyright: Sigeki Noya, 1998.

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Correction of Eng. tr. of book title: „The Infinity-Theory Classes“.

Now, let me tell you what that picture means.

The diagonal line in the picture means the diagonal line in Cantor’s dm and all the other possible self-referential statements:

1) that the n-th digit of a countable real number in the dm table is or is not a[n],

2) that the n-th set is or is not included in the n-th set,

3) that the n-th statement refers or does not refer to its own truth-ness,

4) that the n-th statement says or does not say that it itself is provable,

5) etc.

The parallel line B. I was talking about in the page 4 of our conversation „February 2022“ on the Forums.Wordreference.com is named/called in the picture: the straight line S[R].

There is a mapping from the diagonal onto B = S[R] that reverses the truth values like this:

from P to P‘: the truth values of the statements meant by P are 0, so P‘ accepts them as a truth = 1 and registers (as a part of B = S[R]) the negative forms of the statements chosen from among the above 1) – 5).

from Q to Q‘: the truth values of the statements shown by Q are 1, so Q‘ negates/reverses them as a falsehood = 0 and registers (as a part of B = S[R]) the negative forms of the statements from among the above 1) – 5).

Thus, B = S[R] becomes the expression of the complete collections/conjunctions of all the infinite numbers of the negative forms of all the infinite numbers of possible self-referential statements from among the above 1) – 5).

But if such mathematical object B = S[R] could be justified,

then it should be meaning that the conjunctions of only the negations such as :

1) that no n-th digit of a countable real number in the dm table is a[n],

2) that no n-th set is included in itself,

3) that no n-th statement can tell its own truth-ness,

4) that no n-th statement can tell its own provability,

5) etc.,

(which is obviously wrong,) could be also justified.

So, it is a contradiction. Therefore, all the dm’s are wrong.

The dm camp/scholars meant/intended to show that the point R = R‘ meant the self-contradiction of the assumption of the statement that they tried to disprove. Because that the point R = R‘ could mean that the statements meant by the point can neither affirm nor negate themselves;

if their truth values are 0, then they get and do not get reversed to 1,

and if their truth values are 1, then they get and do not get reversed to 0,

thus the truth values would be 0 = 0 = 1 = 1 = 0 and 1.

So, it was intended to have meant the self-contradiction of the asumption.

But as I showed above, the existence of such a line B = S[R] is IMpossible in this world from the beginning; such a line should ( = is supposed to) mean the negation of all the possible self-referential statements in the math in general in the same manner that the dm-line/school mathematicians used in order to mean the „actual existence“ of the complete infinite conjunctions of only the negative cases/forms selected from among the choices between the affirmative statements and the negative statements in the above 1) – 5).

Addition:

Cantor’s dm can be shown to be using a collection of self-referential statements like below:

(We go binary = think in/with the binary notation system.)

There are mappings like the below from the binary r[n]’s ( = Er-ennz: the plural form of r[n]) onto 0 or 1 expressing the non-inclusions or inclusions into C = some „Cantor’s-dm set,“ so to say:

n = 1011101 ↦ a[n] = 0 = not included in C.

and

n = 111111101111 ↦ a[n] = 1 = included in C.

Thus, following the above assumption, you can interpret Cantor’s dm as a collection of self-referential statements on natural numbers such as these:

If the fact is that n = 1011101, then the fact has a nature of „Cantorean-ness,“ so to speak.

and

If the fact is that n = 111111101111, then the fact fails to have Cantorean-ness.

In short, the function

f: the diagonal → the horizontal line B = S[R]

is the all-the-relations-affirmations-negating-and-all-the-relations-negations-confirming function = the all-the-relations-negating function, which is logically unreal/nonsensical.

And dm-line mathematicians tried to „criticize“ the contradictions of the possibility and impossibility of the existence of the intersection point of the diagonal and the horizontal S[R]-line, which would mean both the affirmations and the negations of the relations in question.

But the self-contradictory is THEIR own assumption of the universal/everything-negations in logic; Satanic know-nothing-ist chaos/chaotic theory that says everything is false, uncertain, unknowable, and invalid = unprovable, namely chaotic, for any possible and actual/real/physikalische cognitive subjecta/subjectums including The Omnipresent All-Knower Almighty Infinity God.

For the consequences of the unique/the_only-actual-Infinity existence proofs, the disproofs of the „chaotic or complex dynamical systems“ notions, etc. etc., please see my earlier postings here below and in our Conversations on the Forum.WordReference.com site.

Because the diagonal signifies/denotes all the self-references by the y=x function relating all possible x in the X axis/set to all possible y (= x-itself) in the Y axis/set.

The most essential part on the above was missing:

Dm = diagonal argument.

Dm-d = diagonal argument disproof.

Excuse me, folks!

Sorry. Correction:

Dm = diagonal method.

Dm-d = diagonal method disproof.

Exactly speaking, Cantor’s diagonal methods are said to mean both his „first/erste diagonal method“ and his „second/zweite diagonal method,“ also according to the German Wikipedia. But even more exactly speaking, the first one does NOT use any dm-table-square diagonal-lines per se; therefore, most authors and I count it out as a diagonal method.

The firstly-shown dm-d here handles one of the UNIVERSAL dm (I would like to re-interpret „dm“ as „diagonal-methodS“ in the plural, not „diagonal method“ in the singular.) including their equivalents of all the self-referential paradoxes, and puts forth the UNIVERSAL dm-d (diagonal-methodS disproofS).

Note:

An anonymous Japanese „Mr. Taikakusen-Ronpoo Bokumetsu Keikaku = Mr. Dm Extermination Project“ on his blog site has a few other branches of valid universal dm-d of his own inventions. But at present, his site is exclusive = a site that only the people he lets view it can view.

Correction:

puts forth the UNIVERSAL dm-d

→

puts forth one of the UNIVERSAL dm-d, other than those of Mr. Taikakusen-Ronpoo Bokumetsu Keikaku.

Thanks for clarifiying this. The first diagonal method is not problematic, and strictly spaking, it is even not really a diagonal method, It is more like a spirale method.

The second one is the problematic one.

I can very simply show that it is problematic:

In real numbers 0.999…=1.000

Both have not a single digit in common but are the same number in real numbers. (This does not hold in other systems like surreal numbers or hyperreal numbers.)

If two numbers may be equal without sharing even one common digit, the dm method does not work, at least it does not work well.

Thank you very much, Koiti, for providing this.

Dm-d corollary = Mathematico-physikalische/physical Apologetics 1: The Offense

Cf.:

((((Deep Riemann Hypothesis Theorem. ⇔ Riemann Hypothesis Theorem. ⇔ BSD Hypothesis Theorem.). ∧ (dm-d. ⇔ (Zeta functions unification. ⇔ Generalized Riemann Hypothesis Theorem. ⇔ Artin Hypothesis Theorem. ⇔ actual infinities non-existence proof. ⇔ dm-d-aided discrete analytics universality proof. ⇔ Nakai’s discrete analytics universality proof. ). ). ). ∧ Kawada’s circle method. ). ). ). ). ⇔ Goldbach Hypothesis Theorem. ⇔ Twin Primes Theorem. ⇔ Kawamura’s twin primes generating function. ⇔ Kawamura’s primes generating algorithm. ⇔ Kanno’s primes generating algorithm. ⇔ P=NP proofs. ⇔ dm-d-aided P≠NP disproofs. ⇔ PTT ( = Pythagorean-like theorems theory. = universal/versatile/all-purpose Diophantine equation solution theory). ⇔ Goedel-Matiyasevich’s Hilbert-10th-Problem „solution“ disproof. ⇔ God’s omniscience proofs. ⇔ God’s infinite CPU-and-memory sizes proof. ⇔ God’s eternal omnipresent ( = infinitely-extending) and omnipotent ( = immanent and transcendent) Creator/Controler/Judge-ness proofs. ⇔ Proof of the existence of the unique/one-and-only infinite/unlimited God with infinite resources/“powers“. ⇔ Proof of God’s ultimate victory over evil spirits(-ed people) including Satan. ⇔ Lee Strobel’s plus Arimasa Kubo’s plus Werner Gitt’s plus Richard Jack’s apologetics minus its parts based on the below „Apologetics 2: The Defense“. ⇔ Chrstianity truth-ness proof.

Correction:

Read „parts based on“ in the last line but one as „parts criticized in“.

Nakai’s calculus was not any discrete calculus; Nakai’s calculus only uses dt=1 for all the independent variables t.

Correction:

Read „actual infinities non-existence proof.“ as „Actual infinitesimals non-existence proof.“ .

Sorry again!

Dm-d corollary = Math-Phys Apologetics 2: The Defense

You ( = the general/generic „you“ including Deiner/Dich, Bernd) must cast away the whole system of the literally chaotic theory = chaotic pseudo-sciences/“TOE ( = Theory of Everything)/SGUT ( = Super Grand Unification Theory)“ which have/has branches/disciplines equivalent to/with each other:

chaos = undiscernibility of A from non-A = „0 A-ness = 1 A-ness.“ = dm-aided “ ‚0=1.‘ proof“ = dm = existence of actual infinitesimals = existence of infinite kinds of infinities ( = unlimited evil/chaotic/vandal gods over creatures) = Incompleteness/Inconsistency Theorem = non-existence of all-knowing, all-possible-to-do-good God = paraconsistent/inconsistent Diamat ( = dialectical materialism/Marxism) = „kg^1 * m^0 = kg^1 * m^1.“ (another „0=1.“) = „E=mc^2.“ = TR ( = theories of relativity) = U ( = uncertainty/unpredictability/un-analyzability/chaoticity) = existence of quasi-static/infinitesimal thermo-dynamical changes = the universality of the chaos with ever-increasing entropies = modern „phys“-based cosmology: Vibrating or Ever-Swelling Universe/Multiverses ending up in either Big Crunch(es) or themal death(s) or tearing-up(s)/ripping-up(s) of itself/themselves = desperationist/hedonist „natural history“/“biohistory“ world-view like in the Preface of „Die Dialektik der Natur (The Dialectics of The Nature)“ by Engels = existence of undefined „emergences“ including macro-evolutions = denial of the existence of the Creator/Controller/Judge = evolutionist linguistics ( = either TGG or „cognitive semantics“ supported by construction grammar that is equivalent to TGG) for strong-AI-making tries = the ignoring of the Ugly Duckling Theorem = the ignoring of the frame problem requiring the classifications/judgements of relevant and irrelevant information pieces = the negation of George Bealer’s mathematical proof of the existence of non-physiological minds = the denial of the existence of souls/Seelen including the triune God and evil-spirits under Satan = the rejection of Christianity.

Dm-d corollary = MPA 2: The Defense (continued)

dm = „0=1.“ = „For all x such that x>0 or x0 or x<0, curvature 0 = curvature(s) x." = the denial of the Parallel Line Theorem (not Axiom) = the acceptance of non-Euclidean geometries = TR ( = theories of relativity) = the rejection of Yasuharu Hamaoka's proof of the finite size of the non-spirit-matter universe (not of the physical space itself) = the nullification attempt against the infinite Ausdehnungen/extensions of the absolute time and absolute space = the denial of the eternal and omnipresent infinite God enclosing/encasing the whole universe = the negation of God's infinite resources including his infinite energies storage, his infinite "eyes and hands," his infinite memories, his infinite CPUs, and his infinite past contemplations/calculations/plannings about the infinite eternal future motions of all the particles in/of the whole universe

= TR-cosmology's "solution" of Olbers's Paradox = the negation of Seeliger's Paradox

= the rejection of the fact that God exists as an entire-universe-permeating/omnipresent, immanent AND transcendent entity/subjectum among all the matters/particles of the whole finite universe AND even outside of the finite universe as well, in His size of the only infinity.

Thus, I would like to shout to the world like the little child in the last scene of Hans Christian Andersen's fairy tale, "Emperor's New Clothes":

"He ( = The atheism/pantheism) has got nothing on ( = wearing nothing) ! "

Only the supporters of the Emperor ( = the anti-Christianity) says that he looks splendid in his new clothes ( = modern pseudo-sciences), but actually he is naked !

Correction:

Read the first and second line above as:

dm = „0=1.“ = „For all x such that x>0 or x0 or x<0, curvature 0 = curvature(s) x."

Re-correction:

Read the above „x0 or x<0," as:

"x<0, x=0." = "

Re-correction:

Delete the above „or x0“.

Read „on the Forums.Wordreference.com“

as „on the Forums.Wordreference.com website“.

Wordings corrections:

Read „discrete analytics“ as „discrete calculus“. Cf. below:

https://en.wikipedia.org/wiki/Discrete_calculus

Delete „PTT ( = Pythagorean-like Theorems Theory“ and insert

„Dest“ in the place of the above deleted acronym plus phrase.

(Otherwise, you could easily mix up PTT with TPP.)

You can see also one of my Dest ( = Diophantine equations solutions theory) branches so easily: It’s another fool-proof math piece!

As you can see from the below link, the following Telephone-Numbers theory and Hosoya-Indexes theory determine the configurations and numbers-breakdowns of all the possible Young tableaux, and therefore, simultaneously, those of all the possible n-D hyper-polytopes as n-D compounds/assemblages of those Young tableaux pieces/tiles with the thicknesses of 1 ( = one):

Telephone number (mathematics) – Wikipedia

Hosoya index – Wikipedia

Therefore, the equi-hypervolume ( = equal hyper-volume) transformations of the hyper-polytopes represented by their-hyper-volumes-expressing polynomials (with only natural-number coefficients) A and B, as expressed in the equations

A = B.

⇔

A — (minus) B = 0.

can all be solved as natural-number-solutions-Diophantine equations.

And the A+B=0 problem solves itself in the same way as in the way for A-B=0:

You know my variables-kinds-number reduction method by the assumed mean x or x[1] and by turning x[n] into (x – a[n]), taking the differences between x[1] and x[n] = a[n] . Thus, you can handle only one-variabled Diophantine equations. And if x could take any positive solutions, then the equations would have to get some -B sum part. That leaves as the problem the cases of the equations with only negative-integer x-solutions.. But in that case, you can regard the „(coefficients)*(x^odd-numbers)“-terms as the negative +B<0.

The end.

Now you see that all the Diophantine equations can be solved at least in one way. I have some more ways.

So, all the codes on Earth will be once cracked and Die Offenbarung Kapitel 18 will come true! Governments already know that and are going be hackers themselves; they all have recently been conspiring to make digital-currencies-only societies to rob everybody of all their assets to force them to enroll in the troops for the World War 3 ending in the Armageddon Battle.

Summary of MPA:

0 chaos = dm-d = TR-d = discrete difference equations universality + Dest = God's omnipresent, omniscient, omnipotent Control = Judgements including Last Judgement.

&

0 chaos = 0 emergence = 0 macro-evolution = Creationism = God's all-initial-data perceivability = God's all-interim-data perceivability = God's omnipresence + (dm-d = ) God's unique infinite CPU-&-memory size and unique infinite energy amount = God's unique eternal-universe-future-planning ability = ditto.

&

3LLNs (3 Laws of Large Numbers) = ditto. .

Framework correction:

dm-d = If an actually infinite cardinal exist, it must be unique.

+

CTOT-d ( = Cantorean transfinite ordinals theory disproof) = If an actually infinite ordinal exist, it must be unique. (See below.)

⇔

If an actually infinite cardinal and an actually infinite ordinal exist, it must be a unique cardinal=ordinal = an actual infinity.

+

Proof of „Theorem ( = not Axiom ! ) of The Principle of The Mathematical Inductions“ by Prof. Shigeru Iitaka (Ee-ee-tah-kah)

= If Peano Arithmetic is consistent and perfect, an actual infinity exists.

+

Goedel’s-dm ( = his „Diagonalization Lemma“ for his „Incompleteness Theorem“) d ( = disproofs) = Peano Arithmetic is consistent and perfect.

=

A unique actual infinity ( = a unique unlimited/unrestricted entity = God) exists.

CTOT-d:

Let d(P, Q) denote the distance between points P and Q on the Euclidean plane with a coordinate system.

If an actually infinite ordinal ω exists, then

d ( P(-ω, 0), Q(+1, 0) ) = ω＋１

＝

d ( R (-1, 0), S(+ω, 0) ) = 1 + ω

＝

ω.

（∵ A part of Cantor’s own actually-infinite ordinals calculation methods.)

Addition:

One of the simplest dm-d’s:

dm-d. ⇔ d ( = disproof) of Goedel’s „Diagonalization Lemma“ for his „Incompleteness Theorem“. = d of the contradiction of the Lemma’s assumption of „G = not-Provable(G). ⇔ not-G = Provable(G) = G.“.

Correction:

Read „set“ in „And let the minimal set ( = the least set) of S[0] be n[0].“ as „element“.

Actual-infinity-existence. = MIPT (mathematical-inductions-principle theorem) = (dm-d = TR-d = PLT [parallel lines theorem] = Seeliger’s Paradox).

The „equals“ show equivalencies.

I’ll never repeat that again even for you; so, please please try hard to memorize that.

The proof of the above MIPT that was halfway-done by Prof Shigeru Iitaka ( = Ee-ee-tah-kah) and complemented/modified by me:

The source is Shigeru Iitaka: „Let’s Start Math Researches, Vol. 4: The New World of Perfect/Complete Numbers“ (in Japanese)

(Kyoto: Gen-dai Suu-gaku Sha, 2017), pp. 121, f.

The def. of MIP:

If and if only the subset S of N = {0,1,2,3,4,5, …} satisfies the following conditions of attributes/natures and , then S = N.

: 0 ∈ S.

: If n ∈Ｓ, then n+1 ∈ S.

The def. of the minimal element of S:

n such that n ∈ S is the minimal element of S, if and only if:

either

1) n = 0,

or

2) if there exists an n‘ such that n = n‘ + 1, then n‘ ∉ S.

The existence of minimal elements in all non-empty set S:

„If S is not empty, S has a minimal element.“

Prof Iitaka assumes that the above statement must remain an axiom, saying that the proof of the following theorem:

„For all S, S has the least element.“

needs the proofs of all the ideas about the order in N, by MIPT itself.

But that is wrong because the above statement is a provable theorem:

because 1.: by the axioms of PA, for all n such that n ∈ S, n<n+1<n+2<n+3< … .

and

because 2.: for all S and for an existent n, n ∈ S.

(Namely, 1. tied up with 2. means that n must be the least element of S.)

Now the proof of MIPT, which is that "S = N." by contradiction:

Let S be a subset satisfying the above natures and .

And let S[0] be S[0] = N\S.

And let the minimal set ( = the least set) of S[0] be n[0].

From the above minimal-element def. 1), n[0]>0.

From the above minimal-element def. 2) and the above n[0] ≠ 0, there exists an m such that n[0] = m+1.

From the def. of the minimal element, m ∉ S; so, m ∈ S.

From the above nature of S, n[0] = m+1 ∈ S.

Therefore, n[0] ∉ S.

That contradicts the assumption: n[0] ∈ S.

So, S[0] fails to exist.

Thus, S[0] = N\S = N – S = Φ.

Hence, N = S.

QED.

Correction:

Delete „and“ from right before „then S = N.“.

Insert „1.“ and „2.“ between „then S = N.“ and the following colons.

One of my RH ( = Riemann Hypothesis) Theorem proofs:

Chen’s theorem II ( = 2) ⇔ Primes sequence quasi-„randomness“ including Twin Primes Theorem ⇔ RH Theorem.

The proof of the first equivalency above:

Chen’s theorem – Wikipedia

In Chen’s theorem II ( = 2), the whole number of the occurrences that „among all the A∞ ( = actually infinite) numbers of the pairs of (p, p+h), some (p+h) are the products of two primes“ is A∞. But the whole number of the occurrences that „among all the A∞ number of pairs of (p, p+h), the rest of the (p+h) [ = other (p+h) ] are just-one-single primes“ is also (A∞ – A∞) = A∞.

So, for all the primes p, for all the even numbers h, and for all the (p, p+h) pairs, the pairs with the just-one-single primes (p+h) abound A∞-ly ( = actually infinitely) many.

Thus, for any intervals of the widths of even numbers of h within the natural numbers scale/line, there always exists at least one prime.

That means that the intervals of the occurrences of the two consecutive primes seem totally „random/chaotic“.

(For the proof of Twin Primes Theorem, apply the ‚h = 2.‘-case.)

The proof of the second equivalency above = RH proof by primes-„random“-ness:

It would be too long to write here; so, please read the outline in John Derbyshire: „Prime Obsession,“ chapter 15 and chapter 20, section VI for yourself.

Prime Obsession: Bernhard Riemann and the Greatest Unsolved Problem in Mathematics: Amazon.de: Derbyshire, John: Bücher

Correction:

Read „for all the primes p“ as „for an infinite number of primes p“.

The neo-natural/scientific theology books that I recommend:

1. René Descartes: „Discourse on Method“

2. Richard Jack: „Mathematical Principles of Theology“

3. Akiya Nakai: „Ryoo-hen ni Integuraru Tsuke-chatte Ii ( = Ee-ee) no? = Can You Put Integral-Signs on the Both Sides of Equations?“ (Proof of the existence of the mathematico-physical „God-variable“ regulating all the other variables, in connection with discrete calculus = sum and difference calculation instead of continuous calculus = integration and differentiation. A fairly easy math book in the Japanese language. Paperback edition also available. Please Google-translate this: )

Amazon.co.jp: 両辺に∫（インテグラル）つけちゃっていいの？ 第二版: 高校では教えないが、大学でも教えてくれない微積の読み方 eBook: 中井晶也: Kindle Store

4. Werner Gitt: „Without Excuse“ (Revised edition of the below 5. . German translation: „Information“)

5. Werner Gitt: „In the Beginning Was Information“ (German original: „Am Anfang war Information“)

6. Arimasa Kubo: „Science Comes Closer to The Bible“ (in English)

7. Benjamin Wiker and Jonathan Witt: „A Meaningful World“

8. Jonathan Wells: „Icons of Evolution“

9. Nicholas Humphrey: „Seeing Red“ (Proof of the blind sight = souls‘ sight without the help of the brain)

10. Emma Byrne: „Swearing Is Good for You“ (Proof of the mute speeches = souls‘ speeches without the help of the brain, and proof of the existence of demon-possessions)

11. Constantin Virgil Negoita: „Post Modern Logic“ (Proof of the existence of Satanists = Luciferianists)

12. Stefano Mancuso: „Brilliant Green: The Surprising History and Science of Plant Intelligence“

13. Lee Strobel: „The Case for A Creator“

14. Lee Strobel: „The Case for Christ“ (German translation: „Der Fall Jesus“)

15. Lee Strobel: „The Case for The Real Jesus“

16. Lee Strobel: „The Case for Faith“

17. Lee Strobel: „The Case for Grace“

18. Lee Strobel: „The Case for Hope“

19. James D. Long: „Riddle of the Exodus“ (Proof of the fact-ness of the Exodus)

20. Mark C. Mattes: „Martin Luther’s Theology of Beauty“

21. Mark S. Sooy: „Essays on Martin Luther’s Theology of Music“

22. Mother Basilea Schlink: „Rock Music: Where from? Where to?“ (Proof of the demon-possessed nature of the beat-music, especially one using the blues-notes/modes and the blues-chords. Please Google also for the history of the blues and of the jazz, the Islamic origin of the blues, the anti-Christian/anti-scientific characteristics of the Arab music.)

The book on the Arab music that I recommend:

That book shows that the Arab modes/scales include almost or totally the same tones as the blues-notes/mode/scale. And the book also reveals that the Arab music rejects/defies all musicology; the Arab music only consists of ad-lib solo singings: no harmony, no ensemble, and no fixed forms. It is anti-science including anti-aesthetics = anti-Lutheran/Cartesian/Newtonian = anti-theology = anti-reason/Vernunft = anti-Holy-Spirit.

The Amazon.com page fails to show the book, therefore, here is the Abebooks page:

https://www.abebooks.com/book-search/title/musique-arabe/author/jargy-simon/

I like arab poetry and music and blues. I like many kinds of music.

23. Joseph N. Manago: „Mathematical Logic and the Philosophy of God and Man“

Amazon.co.jp: Mathematical Logic and the Philosophy of God and Man: Manago, Joseph N.: 洋書

Google-translate my book-review that will be shown soon. I wrote there that the book’s only wrong parts are based on Manago’s dependence on Leibniz’s monadological premises that souls are no matters (that contradicts the fact of the dualist-materialism) and that the attributes of the souls can be cognized in no time at all.

(Manago cites the modern phys „theories,“ but does not at all use them for his arguments. So, that part has few problems.)

Correction of 5.:

German original title: „Am Anfang war die Information“.

23. Joseph N. Manago: „Mathematical Logic and the Philosophy of God and Man“

Amazon.co.jp: Mathematical Logic and the Philosophy of God and Man: Manago, Joseph N.: 洋書

Google-translate my book-review that will be shown soon. I wrote there that the book’s only wrong parts are based on Manago’s dependence on Leibniz’s monadological premises that souls are no matters (that contradicts the fact of the dualist-materialism) and that the attributes of the souls can be cognized in no time at all.

(Manago cites the modern phys „theories,“ but does not at all use them for his arguments. So, that part has few problems.)

A truly complete branch of Esst (= equations-systems solution theory):

The branch was, I have found, already made by Toshikazu Sunada: „Bunkatsu no Kika-gaku: Deen ni Yo-ru 2(Huta)-tsu no Teeri ( = Geom. of Decompositions: 2 Theorems Due to Dehn)“ (Tokyo, Nihon Hyooron-Sha, 2000).

Sunada says that complex discrete Laplacians for weighted-graphs help solve any circuit-decomposition problems of any AC circuits with any electrical elements, not alone with resistors.

That means, you can solve the decomposition-problems for any overlaps-allowing ( = ±-terms representing) hetero-magical graphs (representing any holes-&-overlaps-allowing hyper-varieties, which further represent any equations in any equations-systems.)

In addition, such overlaps can be seen as part of weighted/colored hypergraphs, too.

The above proves the „self-fulfilling-prophecy“-ness of Revelations Chapter 18 at the end of The New Testament by the quick-solvability of any equations-systems for the cracks of any codes, both present and future ones, resulting in the fall of Satanists’/capitalists‘ „Babylon“ Imperialist World-Empire relying on the ubiquitous-ICT infrastructures.

The discrete math suffices for the cracks. The reasons are two-fold:

1. The only justifiable/orthodox analytics was proven to be the discrete calculus in the afore-mentioned book by Akiya Nakai.

2. And the real numbers are merely shorthands/abbreviations of their expansion-formulas (or computation tools) for the Diophantine approximations applied to the problems concerning the discrete physical/physikalischen realities.

And because it is a graph-theoretical solution, you can expand the cubing into the hyper-cubing; you can pop up/aufklappen the 2D graphs into nD ones, like pop-up cards or pop-up-books/Aufklappbücher.

And hyper-cuboid-ing can be solved by seeing hyper-cuboids as rows of hyper-cubes.

It is interesting that Zenon’s paradox remains paradox.

It is basically: a point is not a distance.

No, as I shared with you a few days ago, the converging actually-infinite fraction expansions do exist: for example, in one of Zeno’s pseudo-/seeming-paradox, Achilles‘ steps converge and catch up with the turtle’s, because, the shorter the steps, the less time they take; no actually-infinite time-period is required for the catch-up (which sounds like ketchup).

RSA is now completely out.

A new book by Frau Professor Hukiyo Kobayashi: „Oiraa kara Hajimaru Hushigi na Sosuu no Mitsuke-kata = Mysterious Ways to Find Prime-Numbers Beginning with Euler(’s Math)“ (Gijutsu-Hyooron Sha, 2021) has publicized perfect primes-generating formulas that she herself calls „RSA-cracking“ formulas (p. 204).

(It is NOT on the pseudo-primes-formula or primes-formula-try by Euler himself that generated only the first 40 primes.)

And now my Esst against any post-RSA codes (with the coming QCs = quantum computers)!

The capitalism is doomed to get torn down, as in Revelation 18; their only way out is the also-prophesied Final World War ending up in the Armageddon Battle against the invincible angels-troops of billions of immortal angel-soldiers.

Perfection of magic-hypergraphs-aided Esst branch

Re:

1. Hadwiger-Nelson-Problem – Wikipedia

2. Decades-Old Graph Problem Yields to Amateur Mathematician | Quanta Magazine

3. Wayback Machine

Since the absurd AC (= Axiom of Choice), equivalent with dm (= diagonal-methods), has now been nullified by my dm-d (= diagonal-methods disproofs) and AC implies DC, the corrected H-N problem solution is the four-colorability even for any infinite planar unit-distance graphs.

The above corrected H-N-Problem solution means that we have another perfect Esst branch using hypergraphs relying only on the present version of Dr. Kasper Mueller’s +/-/*/division-operations-graphs and Sugiyama’s magical-hypergraphs construction method:

1. Corrected H-N-Prob solution: you can 4-color all the infinite graphs including the ones in the above treatises on H-N-Prob or their dual graphs.

2. Therefore, the minimum chromatic numbers for the Mueller-advocated graph-theoretical ops-visualization method is four, namely the colors for the four basic arithmetic ops.

3. Hypergraphs consisting of */division-ops-edges scooping/picking up variables with the exponents/power-indexes of 1’s and grouping/tying/wrapping them together as variables-powers-products and also consisting of +/- ops-hyperedges tying those edges and other single variables with the exponents of 1’s can be seen as a kind of the „dual graphs“ mentioned in the above 1.

They are like this (the hyphens stand for *-edges, the =’s for +-ones, the ~’s for subtraction-ones, and the #’s for division-ones):

x1-x1-x1 (x1^3)-x2 ~ x1-x1-x1-x1-x3-x3#x4 = x1-x1-x3-x4#x5-x5 = … ~ … .

4. And they do not have to be directed hypergraphs only if you specify the upstream/downstream-directions in two dimensions among the graphs-dimensions, for the directions of x-y (not y-x) and x:y (not y:x).

5. Those hypergraphs can be, of course, weighted magic ones with the magic sums of 0’s.

6. Sugiyama, in his treatise entitled „Generalization of magic graphs and their properties“ actually showed the magic hypergraphs construction method all right.

The Mueller method:

Visualizing Mathematical Equations and Operations|Medium.com

The Sugiyama method:

情報学広場：情報処理学会電子図書館 (Press the „pdf“ button.)

And the above pseudo-proof for the pseudo-solution also contradict 4CT (= Four-Coloring Theorem):

4CT works. Therefore, some of its proofs should include the inferences by MIPT (= Mathematical Inductions Principle Theorem). So, such proofs ensures 4CT for the graphs and their dual graphs with vertexes/edges number of 1, 2, 3, 4, … , omega = actual infinity. Thus, the above pseudo-proof on the infinite-graphs colorings has been refuted/negated.

Naturally, the adjacent edges for the same kinds of operations in hyperedges as in the above example get the same colors; but you can identify the rows or lumps/bunches/Straeusse of such edges, with single tied-up/wrapped-up vertexes within the whole hypergraphs, so that you can regard the whole hypergraphs as a kind of non-hyper graphs. In that way, all such adjacent vertexes in them get different colors, and 4CT applies for the „graph“.

Books say, you call the above ops-expressing hypergraphs „non-linear mixed hypergraphs“.

The hypergraphs in question are not „linear“ in which „no two edges intersect in more than one vertexes.“ (Syed Ahtsham Ul Haq Bokhary: „Chromacity of Hypergraphs: Chromatic Polynomials and Chromatic Uniqueness of Spernerian Hypergraphs“ [Saarbruecken, Germany: LAP Lambert Academic Publishing, 2011 ], p. 21). The edges and/or hyperedges there can have more than one common additive or multiplicative factors like in the terms of:

x-x-x-y-y

and

x-x-y-y-y-y,

or

x-x=y=z=u=w-w-w

and

x=y=z=w.

(- stands for a *-edge, and = for a +-edge.)

(In both cases, the common edges and hyperedges stand for two terms[-rows] in two different equations in the same equations-system to be solved.)

But „mixed“ they are; edges and of hyperedges of the same colors continue as long as the same operations to be expressed in the hyperedges continue in a row, but where a new operation starts or intervenes, the colors change/switch there:

x-x-x-y=x-y-y has two colors for edges: one for the -(*) edges and another for the =(+) edge. So: mixed. (According to the definition by Vitaly I. Voloshin: „Coloring Mixed Hypergraphs: Theory, Algorithms and Applications“ [Providence, Rhode Island: American Mathematical Society, 2002], p. 3.)

Other Cantorean-dm d that does not rely on Noya’s graph

1. For the criticisms against the notion of „actual infinitesimals,“ see Amir Alexander’s book: „Infinitesimal“.

Still, there must be actually-infinite(-digited) fractions; because otherwise, the real-numbers-theory including the analytics fails to work; and because otherwise, infinite/endless fractions would have ends = the last digits = an actual-infinitesimal multiplied by numbers from 0 to 9.

Even so, the humanly-feasible math must regard such actually-infinite fractions (including the fractions generated by quasi-random generation algorithms) as their potentially-infinite expansion-formulas.

A divinely-feasible math would have algorithms for the generations of genuinely-random fractions (like the binary one whose each digit gets chosen by tossing a coin); because you have the three kinds of (strong, weak, and complete) LLNs (= laws of large numbers). But humans must dismiss/forget/ignore those algorithms as hidden/un-knowable.

Thus, you could biject natural numbers and potentially-infinite binary (or any) real numbers like this:

0, 0.1, 0.01, 0.11, 0.001, 0.011, 0.101, 0.111, 0.0001, 0.0011, 0.0101, 0.0111, 0.1001, 0.1011, … .

2. When you go binary, you can produce only one new Cantorean anti-diagonal binary real number.

Therefore, you could slide the first, second, third, … binary real numbers in Cantor’s dm-table onto the second, third, fouth, … lines. Then you could give the newly-produced anti-diagonal binary real number the serial number of 1. Then you could biject natural numbers and binary real numbers.

Corrections:

Read „dm-d“ in the head-line as „dm-d’s“. Read „does not rely“ there as „do not rely“.

RSA cracks (Ransack) facilitated 1

The first/top formula of the below link No. 2 must make RSA-cracks easy, because Masato Kanno’s „Eratosthenes‘ Sieve Formalization“

uses y=sin(x/n) (where the n’s are natural numbers), whose graphs cross each other only at the x-coordinates of „composite-numbers“ and at the y-coordinate of y=0, and the below argument based on the link No. 2 must help its formula-nization.

The relevant books:

A. Masato Kanno: „Suuji Pazuru (= Cipher Puzzles): SeeK 10“ on sine-curves and primes,

and

B. Masashi Sanae: „Suugaku Tamate-Bako (= Math Treasure Box)“ on sines/cosines-products integrals mentioned below.

This Youtube video down below in this link No. 1 also shows the principle in the above book A, even without the captions:

No. 1

リーマン予想 証明完了！ : 発想力教育研究所 素数誕生のメカニズム

[/QUOTE]

No. 1:

http://blog.livedoor.jp/art32sosuu/archives/42033644.html

The video in question is at the bottom of the page of the link No. 1.

Link No. 2]

Ransack facilitated 2 (= cont. 1):

From

ω^k = cos{(2k*pi)/n} + i*sin{(2k*pi)/n}

and

the above link No. 2,

follows that:

in order to avoid the below-shown contradiction, you must exclude the cases of the x values such that

(#) … x/p[j] ≠ (not equal) 2*k*pi/n (in the above link No. 2, and where p[j] are j-th primes)

out of the integrals of both sides of the first quoted equation for the denominator-exponent = 1 in the above link No. 2.

Iff (= if and only if) not (#),

then, the below three facts that;

1. ∫（sin x/p[j] * sin x/p[m]）dx = ∫（cos x/p[j] * cos x/p[m]）dx = 0,

iff p[j] ≠ p[m];

and

2. ∫（sin x/p[j] *cos x/p[m]）dx = 0;

and

3. y = Σ (sin x/p[j]) = Σ (cos x/p[j]) = 0

at x = (pi * composite-numbers: n*p[j]). ,

would produce the below contradiction:

For all the natural numbers k≧1, l (ell)≧1, and n≧2, and non-negative real numbers x≧0,

F(n)

= Σ[k = 1, n] {1/(1 – ω^k)}

= 1 – [{1- Σ(ω^k)}/{1- Σ(ω^k) ±Σ(Π(ω^k[l])}]

(where all the k[l]’s are unequal).

Therefore, iff not (#), then,

∫[0. ∞] F(m) dm

= ∫[2, ∞] F(n) dn + ∫[0, 2] (m/2) dm

= ∫ [2, ∞] F(n) dn + [(m^2)/4] [0, 2]

= ∫ [0, ∞] Σ(1-ω^k) / Π(1-ω^k) } dn + 2

= ∫ [0, ∞] {Σ1 – Σ(ω^k)}/[1 – Σ(ω^k) ± Σ{Π (ω^k)}] dn + 2

= ∫ [0, ∞] [{(1/2)*n*(n+1) – Σ (ω^k)}/{1- Σ (ω^k)}] dn + 2

= ∫ [0, ∞] {(1/2)*n*(n+1)} dn + 2

≠ ∫[0, 2] {(n-1)/2} dn + 2,

which would have had to be computed according to Sam Walters in the above link No. 2.

Because,

iff

n≧2,

x ≠ p[j].

and

(2*k*pi)/n = x/p[j].,

then

A

= ∫ [0, ∞] Σ [k = 0, n] [cos {(2*k*pi)/n}] dn

= Σ [sin {(2*k*pi)/n}]

= 0.

and

B

= ∫ [0, ∞] Σ [k =0, n] [i*sin {2*k*pi/n}] dn

= – Σ [i*cos {(2*k*pi)/n}]

= (-i +i) + (-i +i) + (-i +i) + …

= 0.,

and, therefore,

∫ [0, ∞] {Σ (ω^k)} dn

= A + B

= 0.

Because the multiplied sines/cosines need integrations to make them 0, but the added infinite numbers of (infinite Stuecke von) sines and cosines ARE equal to 0 even before the integrations;

because,

iff

for all j’s, m’s and x[m]’s ≧ 0,

x[m] ≠ p[j] ∊ {prime numbers},

then,

Σ [m = 1, ∞] sin (x[m]/p[j])

= Σ [m = 1, ∞] cos (x[m]/p[j])

= 0.

Because sines are actually-infinite/endless periodic regular waves, symmetrical about the x-axis.

Also, cosines are almost symmetrical in the interval of [0, ∞], and you can compensate for the extra bulge in the interval of [0, (pi/2)] later in the interval of [(5/2)*pi, 3*pi] by the negative dent; and similar compensations go on for ever.

Ransack facilitated 3 (= cont. 2):

And because, asymptotically or globally, the sum of the cosines in question in the interval of [0, ∞] should become equal to 0, because ∞ = 2*∞, and so, ∞ can be regarded as if it were an even natural number; there must be an infinite number of the (1 -1)-pairs which make complete the sequence in question into the infinite pairs of the (1 -1)’s adding up to the infinite sum of 0’s = 0+0+0+0+ … = 0 in the grand total.

Ransack facilitated 4:

You can inverse sin nx or cos nx into sin (x/n) or cos (x/n), using the technique for the inversions of complex numbers:

Simple Stuff About Complex Numbers

http://www.consultrsr.net/resources/eis/complex/basics.htm

For the calculations of sin nx or cos nx, you can use Chebyshev’s polynomials:

Tschebyschow-Polynom – Wikipedia

https://en.wikipedia.org/wiki/Chebyshev_polynomials

Correction:

Sorry; you never needed complex-numbers-inversions below to invert p[j]x into x/p[j]: you can simply work/operate the transformation of Y = (1/p[j]^2)*X on the original x.

Simple Stuff About Complex Numbers

A newest primes-generating method(?):

https://www.cantorsparadise.com/finding-primes-using-a-parabola-a939c6e8be53

Auf Medium.com ansehen

This is the everlasting, free-of-charge site showing the above in Japanese:

https://ichi.pro/hobutsusen-o-shiyoshite-sosu-o-mitsukeru-186065615371859

Re-naming:

Esst → Aesst (= algebraic equations systems solution theories).

Because you have also differential and non-algebraic equations-systems.

After Herr Dr. Kasper Mueller on Medium.com website has successfully publicized his graph-theoretical operations- and expressions-visualization theory also for the differentiations and integrations in the near future, then my theories will get back its name of Esst, which is gonna happen for sure. I mean, it’s only a matter/question of time.

Excuse me the frequent hesitations = swaying/shaking to and fro (= back and forth).

What did Goethe say?: „As long as you aspire for betterments/improvements, you hesitate/wander/waver/shake/sway wildly/restlessly/incessantly.“ ?

Hier hab’ ich’s!:

Es irrt der Mensch, so lang‘ er strebt.

(Faust, Der Tragödie erster Teil, Z.317)

This theory must ensure the Esst expansion into a version for the equations systems with Hiroshi-Wada hypercomplex-number coefficients:

„The Remainder Theorem Had a Matrices Version!“:

剰余定理には、行列バージョンがあったんだ！ – hiroyukikojima’s blog (hatenablog.com)

(Mr. Wada’s new book on the matrix expressions of hyper-complexes is forthcoming in a few months.)

My Goldbach Conjecture „proof“ has been found invalid. But here are other people’s seemingly-OK „proofs“:

1. https://leo.aichi-u.ac.jp/~keisoken/research/journal/no113/a/07_KOZU.pdf

2. https://arxiv.org/pdf/math/0103091.pdf

Excuse me. The 1. = Mr. Kozu’s „proof“ has a serious defect; his equation (7) has „a/b,“ which he regards as equal to zero. But it can never be so; because 4=2+2, 6=3+3, 8=3+5, 60=29+31, … , and there abound an infinite number/Anzahl of twin-primes pairs that add together to equal even numbers (because of Kooshiroo Kawamura’s twin-primes generating function formula).