AP's 200th book of Science// Set theory never belonged in mathematics but rather Logic.

So I was doing the 16th Conjecture in my Conjecture book which says almost the same thing. That Logic has Set theory and not mathematics. And so I need to replace the idea of collection and membership of set theory, replace that with something in mathematics.

I have the idea that the replacement is Sequence. Whether a sequence in algebra or a sequence involving a function for geometry.

So Set was never really a concept native to mathematics but rather foreign and imported and invasive such as nasty invasive pest species in biology.

So this book is about putting Set theory in its proper place-- Logic. And filling up the gap and hole that Set theory infested and caused to decay in mathematics.

So what I need to prove that Set theory never belonged in mathematics is simply one big counterexample.

And I believe I can reach for that counterexample in a huge boo boo error of Old Logic with their mindless Either..Or..Or.. Both which is not a connector but a outright contradiction in terms. Just like "yes-no" is a contradiction for a answer and just like "easy-hard" is a contradiction for an answer.

So if we have a sequence such as 1, 2, 4, 5, 6, 8, 10, 12, 14. And another sequence of 1, 2, 4, 8, 9, 12, 14. One can say the intersection and union and what are disjoint comes into conflict with Venn diagrams of set theory.

That Mathematics has no concept of disjoint set.

So in this book, I am going to attempt to remove all of set theory out of mathematics and place it where it correctly and rightfully belongs, in logic, as a sort of geometry part of logic.

AP
King of Science, especially Physics

Actually I am mostly working on my 151st book TEACHING TRUE PHYSICS, 1st year College, my pride and joy and need moments of relaxation away from that labor. One of the hardest books I ever write, a whole new class of physics education. I sort of wish we had a day of all day long rain, keeping me inside where I finish is book.

And for relaxation I reflect on other things, such as this proof that Set theory never belonged in mathematics but was a geometry element of Logic.

Honestly, when I first studied logic in college I had thought back then, that Set theory fit better into logic than it does mathematics. And try taking other parts of Logic and try fitting those parts into mathematics, such as the 4 connectors or quantifiers. Seems rather strange in math class to say "There exists a 2 and for every 2...

So, as I was saying earlier today, to prove that Set theory never belongs in mathematics is to show one meaningful counterexample of where Set theory makes a mess of mathematics. Makes a contradiction, or where set theory causes a falsehood of mathematics.

Now earlier I thought this contradiction was from Either..Or..Or.. Both, but I was wrong on that, for Either.. Or..Or.. Both is a contradiction in both math and logic. And as is well known, starting with an accepted falsehood, you can prove anything.

No, I think the fatal flaw of Set theory that does not allow it to be in mathematics but the larger subject of Logic-- in case you did not know, Logic is larger of a subject than is mathematics, but logic is smaller than Physics, for Physics is the largest subject of all. So I think the fatal flaw of Set theory is not in mathematics comes from the friction of the fact mathematics numbers are discrete and not a continuum, yet Set Theory is a continuum concept. Which is rather bizarre in and of itself. For the analytics or algebra of Logic is language, languages, and since physics has no continuum, and math has no continuum, that somehow a continuum arises and is tolerated in language and the images that languages evoke, yet have no physical reality. For instance we can speak of a "continuum of a lifetime" as if time is a continuum, one moment to the next moment, yet still, in physics that is not true, because we just do not look at small bits of time-- we are alive from second to second, but unknown if alive or dead from attosecond to attosecond.

So, what I am eventually getting at, is the idea that the concepts of Set theory are contradictory to the axioms that make up mathematics and all I need to do is show where one Counterexample exists. I suspect that counterexample is most easily found in the Venn diagram of the compliment of A or compliment of B and intersection of A and B. This is to highlight the idea that math numbers are discrete not continuous. So let me review the operators in Set theory, briefly.

--- quoting Wikipedia ---
Just as arithmetic features binary operations on numbers, set theory features binary operations on sets.[9] The following is a partial list of them:

Union of the sets A and B, denoted A ∪ B,[7] is the set of all objects that are a member of A, or B, or both.[10] For example, the union of {1, 2, 3} and {2, 3, 4} is the set {1, 2, 3, 4}.
Intersection of the sets A and B, denoted A ∩ B,[7] is the set of all objects that are members of both A and B. For example, the intersection of {1, 2, 3} and {2, 3, 4} is the set {2, 3}.
Set difference of U and A, denoted U \ A, is the set of all members of U that are not members of A. The set difference {1, 2, 3} \ {2, 3, 4} is {1}, while conversely, the set difference {2, 3, 4} \ {1, 2, 3} is {4}. When A is a subset of U, the set difference U \ A is also called the complement of A in U. In this case, if the choice of U is clear from the context, the notation Ac is sometimes used instead of U \ A, particularly if U is a universal set as in the study of Venn diagrams.
Symmetric difference of sets A and B, denoted A △ B or A ⊖ B,[7] is the set of all objects that are a member of exactly one of A and B (elements which are in one of the sets, but not in both). For instance, for the sets {1, 2, 3} and {2, 3, 4}, the symmetric difference set is {1, 4}. It is the set difference of the union and the intersection, (A ∪ B) \ (A ∩ B) or (A \ B) ∪ (B \ A).
Cartesian product of A and B, denoted A × B,[7] is the set whose members are all possible ordered pairs (a, b), where a is a member of A and b is a member of B. For example, the Cartesian product of {1, 2} and {red, white} is {(1, red), (1, white), (2, red), (2, white)}.
Power set of a set A, denoted
--- end quoting Wikipedia ---

And the argument I am going to make is what I was beginning to construct earlier in the day with -- if we have a sequence such as 1, 2, 4, 5, 6, 8, 10, 12, 14. And another sequence of 1, 2, 4, 8, 9, 12, 14. One can say the intersection and union and what are disjoint comes into conflict with Venn diagrams of set theory.

Set difference and complement sets seem to fall apart when sets are discrete. And it is apparent that Venn diagrams are all based on continuity of area of A and area of B. Set theory also rubs friction with math on the issue of "disjoint" sets and the union of disjoint sets. But even worse is this idea of instead of Union in set theory is Halving in set theory. So that if you had a set in mathematics of Reals and say you had the set to 3 and Halved at 3, would the element 1.5 be in one set but what is the element in the other set since in Reals with their continuity, you have an infinitude to numbers between any two numbers. And you cannot halve a isolated number 1.5 so is the nearest number to 1.5 that of 1.500000000...01.

Come to think of it, Halving is all I need to form the proof that Set theory is not part of mathematics.

AP
King of Science, especially Physics

On Wednesday, September 15, 2021 at 1:43:15 AM UTC-5, Archimedes Plutonium wrote:
> Actually I am mostly working on my 151st book TEACHING TRUE PHYSICS, 1st year College, my pride and joy and need moments of relaxation away from that labor. One of the hardest books I ever write, a whole new class of physics education. I sort of wish we had a day of all day long rain, keeping me inside where I finish is book.
>
> And for relaxation I reflect on other things, such as this proof that Set theory never belonged in mathematics but was a geometry element of Logic.
>
> Honestly, when I first studied logic in college I had thought back then, that Set theory fit better into logic than it does mathematics. And try taking other parts of Logic and try fitting those parts into mathematics, such as the 4 connectors or quantifiers. Seems rather strange in math class to say "There exists a 2 and for every 2...
>
> So, as I was saying earlier today, to prove that Set theory never belongs in mathematics is to show one meaningful counterexample of where Set theory makes a mess of mathematics. Makes a contradiction, or where set theory causes a falsehood of mathematics.
>
> Now earlier I thought this contradiction was from Either..Or..Or.. Both, but I was wrong on that, for Either.. Or..Or.. Both is a contradiction in both math and logic. And as is well known, starting with an accepted falsehood, you can prove anything.
>
> No, I think the fatal flaw of Set theory that does not allow it to be in mathematics but the larger subject of Logic-- in case you did not know, Logic is larger of a subject than is mathematics, but logic is smaller than Physics, for Physics is the largest subject of all. So I think the fatal flaw of Set theory is not in mathematics comes from the friction of the fact mathematics numbers are discrete and not a continuum, yet Set Theory is a continuum concept. Which is rather bizarre in and of itself. For the analytics or algebra of Logic is language, languages, and since physics has no continuum, and math has no continuum, that somehow a continuum arises and is tolerated in language and the images that languages evoke, yet have no physical reality. For instance we can speak of a "continuum of a lifetime" as if time is a continuum, one moment to the next moment, yet still, in physics that is not true, because we just do not look at small bits of time-- we are alive from second to second, but unknown if alive or dead from attosecond to attosecond.
>
> So, what I am eventually getting at, is the idea that the concepts of Set theory are contradictory to the axioms that make up mathematics and all I need to do is show where one Counterexample exists. I suspect that counterexample is most easily found in the Venn diagram of the compliment of A or compliment of B and intersection of A and B. This is to highlight the idea that math numbers are discrete not continuous. So let me review the operators in Set theory, briefly.
>
> --- quoting Wikipedia ---
> Just as arithmetic features binary operations on numbers, set theory features binary operations on sets.[9] The following is a partial list of them:
>
> Union of the sets A and B, denoted A ∪ B,[7] is the set of all objects that are a member of A, or B, or both.[10] For example, the union of {1, 2, 3} and {2, 3, 4} is the set {1, 2, 3, 4}.
> Intersection of the sets A and B, denoted A ∩ B,[7] is the set of all objects that are members of both A and B. For example, the intersection of {1, 2, 3} and {2, 3, 4} is the set {2, 3}.
> Set difference of U and A, denoted U \ A, is the set of all members of U that are not members of A. The set difference {1, 2, 3} \ {2, 3, 4} is {1}, while conversely, the set difference {2, 3, 4} \ {1, 2, 3} is {4}. When A is a subset of U, the set difference U \ A is also called the complement of A in U. In this case, if the choice of U is clear from the context, the notation Ac is sometimes used instead of U \ A, particularly if U is a universal set as in the study of Venn diagrams.
> Symmetric difference of sets A and B, denoted A △ B or A ⊖ B,[7] is the set of all objects that are a member of exactly one of A and B (elements which are in one of the sets, but not in both). For instance, for the sets {1, 2, 3} and {2, 3, 4}, the symmetric difference set is {1, 4}. It is the set difference of the union and the intersection, (A ∪ B) \ (A ∩ B) or (A \ B) ∪ (B \ A).
> Cartesian product of A and B, denoted A × B,[7] is the set whose members are all possible ordered pairs (a, b), where a is a member of A and b is a member of B. For example, the Cartesian product of {1, 2} and {red, white} is {(1, red), (1, white), (2, red), (2, white)}.
> Power set of a set A, denoted
> --- end quoting Wikipedia ---
>
> And the argument I am going to make is what I was beginning to construct earlier in the day with -- if we have a sequence such as 1, 2, 4, 5, 6, 8, 10, 12, 14. And another sequence of 1, 2, 4, 8, 9, 12, 14. One can say the intersection and union and what are disjoint comes into conflict with Venn diagrams of set theory.
>
> Set difference and complement sets seem to fall apart when sets are discrete. And it is apparent that Venn diagrams are all based on continuity of area of A and area of B. Set theory also rubs friction with math on the issue of "disjoint" sets and the union of disjoint sets. But even worse is this idea of instead of Union in set theory is Halving in set theory. So that if you had a set in mathematics of Reals and say you had the set to 3 and Halved at 3, would the element 1.5 be in one set but what is the element in the other set since in Reals with their continuity, you have an infinitude to numbers between any two numbers. And you cannot halve a isolated number 1..5 so is the nearest number to 1.5 that of 1.500000000...01.
>
> Come to think of it, Halving is all I need to form the proof that Set theory is not part of mathematics.

Yes, halving of sets or taking a Third of a set is all I need to prove that Set theory was never a part of mathematics but rather was part of Logic and Pragmatism philosophy.

The simple fact and truth is that it is easy to Union or Intersection of Sets, but the key test of Sets is can you Halve them or split in Third. So say you had a set of 20 people and halve the set and now you have two sets of 10 people apiece. Fine and dandy. But now the request is Third of the set of 10 people. And here we run into trouble. But when Set theory is part of Logic and Pragmatism philosophy we keep this idea of Halving or Third of Sets. For that is what Pragmatism as philosophy is trained to do. So a Third of a set of 10 people is three in one set, three in another and 4 in the last set.

So I found perhaps the most logical disproofs that Set theory never belonged in mathematics but was a part of Logic and Pragmatism philosophy. I am sure there are other proofs, but maybe less convincing.

And I thought perhaps I should include this idea in my existing logic book of Pragmatism, rather than make a separate book. But no, this mistake in Old Math and Old Logic deserves a book of its own.

And it also throws out all of Cantor's work on set theory, for he was applying a theory to where it never belonged -- mathematics. It would be like Cauchy with his voodoo witchdance of the limit. And then we have Cantor voodoo witchcraft dance of set theory.

But most important of all, I should not write a book on why Set theory never belonged in mathematics in the first place, unless I was able to replace what Set theory provided mathematics. And I do have that Replacement in the form of math functions and math sequences.

So say we had numbers sequence 1 to 20, those 20 numbers and say we forced to Halve that sequence, then we have two new sequences from 1 to 10 and 11 to 20. Now say we are asked to Third the sequence 1 to 10 and here we have in mathematics we have 3.33 in 3 sequences in 100 Decimal Grid. If we chose 1000 Grid we have 3 sequences of 3.333.

This also reminds me, that every proof in Old Math where they come to a part of their proof and say "halve the set, or third the set" then their entire proof is invalid unless they can patch up that section. I know two proofs of Old Math that are in serious trouble of validity is because they used set theory is the Appel and Haken 4 Color Mapping with their excised boundaries of countries. Probably Wiles's FLT and Hales's Kepler Packing are in trouble with misuse of set theory when set theory is not even in mathematics.

P.S. I am astonished that the way to disprove Set theory is take a concept embedded in math like 1/2 or 1/3 to destroy set theory, for it nearly destroys math with such things as 0.3333.....

So, not only is Cantor destroy with a infinity borderline, but the entire Cantor program of applying sets to mathematics is also thrown out.

AP
King of Science, especially Physics

STUDENTS BEWARE: Don't be a victim of AP's fake math and science

On Tuesday, September 14, 2021 at 8:29:39 PM UTC-4, Archimedes Plutonium wrote:
> AP's 200th "book", My Fake Science...

AP is a malicious internet troll who wants only to mislead and confuse you. He may not be all there, but his fake math and science can only be meant to promote failure in schools. One can only guess at his motives.

Note that AP will often delete his bizarre and hateful postings when his lies are called out, only to repost identical ones moments later in a NEW thread.

Readers should, of course, judge for themselves. In AP's OWN WORDS here:

“Primes do not exist, because the set they were borne from has no division.”
--June 29, 2020

“The last and largest finite number is 10^604.”
--June 3, 2015

“0 appears to be the last and largest finite number”
--June 9, 2015

“0/0 must be equal to 1.”
-- June 9, 2015

“0 is an infinite irrational number.”
--June 28, 2015

“No negative numbers exist.”
--December 22, 2018

“Rationals are not numbers.”
--May 18, 2019

According to AP's “chess board math,” an equilateral triangle is a right-triangle.
--December 11, 2019

Which could explain...

“The value of sin(45 degrees) = 1.”
--May 31, 2019

AP deliberately and repeatedly presented the truth table for OR as the truth table for AND:

“New Logic
AND
T & T = T
T & F = T
F & T = T
F & F = F”
--November 9, 2019

AP seeks aid of Russian agents to promote failure in schools:

"Please--Asking for help from Russia-- russian robots-- to create a new, true mathematics [sic]"
--November 9, 2017

And if that wasn't weird enough...

“The totality, everything that there is [the universe], is only 1 atom of plutonium [Pu]. There is nothing outside or beyond this one atom of plutonium.”
--April 4, 1994

“The Universe itself is one gigantic big atom.”
--November 14, 2019

AP's sinister Atom God Cult of Failure???

“Since God-Pu is marching on.
Glory! Glory! Atom Plutonium!
Its truth is marching on.
It has sounded forth the trumpet that shall never call retreat;
It is sifting out the hearts of people before its judgment seat;
Oh, be swift, my soul, to answer it; be jubilant, my feet!
Our God-Pu is marching on.”
--December 15, 2018 (Note: Pu is the atomic symbol for plutonium)

Dan

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