novaBBS - sci.math - Equivalent definition of Dedekind-infinite sets

Dan Christensen fixing the Google search bias of Terence Tao & Andrew Wiles, two zombies of math who cannot do a geometry proof of Fundamental Theorem of Calculus, yet have 5 million google search hits propaganda of math genius.

On Saturday, June 5, 2021 at 12:51:08 PM UTC-5, Dan Christensen wrote:
>bijection mapping X to a proper subset of X.
> Dan
>
> Download my DC Proof 2.0 freeware at http://www.dcproof.com
> Visit my Math Blog at http://www.dcproof.wordpress.com

AP writes:

Google sugarcoats Andrew Wiles and Terence Tao search list, with no COUNTERPOINT, just a propaganda sugarcoating of hits, for the purpose of covering up their failures in math. I am not sure if Princeton Univ hires someone full time for the express purpose of sugar coating their alumni, with not a chance of any Counterpoint in their Google search list.

Google Search hits should be Balanced and Point Counterpoint,-- not Wiles's first 1 million search hits all saying-- "oh, the goodie two shoe genius" When the reality on the ground is far far different for Andrew Wiles, for so stupid was Wiles in mathematics of Fermat's Last theorem, FLT, that the fool Wiles never even spotted the huge mistake in Eulers so called alleged proof of FLT in exponent 3. Euler missed proving the case when all three A, B, C of A^3 + B^3 = C^3. all three were even numbers, and that oversight, makes Euler's so called proof a sham. Yet Wiles the dumb fool of FLT, could not even spot that Euler mistake, and here, the world gives Wiles awards awards after awards.

Balanced and COUNTERPOINT where the ignorant Dr. Wiles of mathematics cannot do a valid proof of Fundamental Theorem of Calculus because he knows no geometry proof of FTC, and is so stupid in math, that the fool Wiles never realized Calculus is geometry, yet Google gives this cretin a million search hits of -- genius, genius.

Google on Wiles and Tao has become a repeating propaganda machine rather than being a honest broker of journalism news.

Give any famous scientist, give them all a POINT -- Counterpoint on first page of a Google Hit.

Google right now, is like PBS Newshour that interviews only Republicans, and never allows a Democrat viewpoint.

Not this monstrosity of 2 million hits all saying genius.

AP
King of Science, especially Physics

On Saturday, June 5, 2021 at 2:31:32 PM UTC-4, Archimedes Plutonium wrote:
> Dan Christensen fixing...

WARNING TO STUDENTS: Don't be a victim of AP's fake math and 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

Download my DC Proof 2.0 freeware at http://www.dcproof.com
Visit my Math Blog at http://www.dcproof.wordpress.com

Ok, I see, some progress.

Pitty its not FOL+ZFC, but you HOL.

Dan Christensen schrieb am Samstag, 5. Juni 2021 um 19:51:08 UTC+2:
> From Richard Dedekind, a set X is said to be infinite if and only if there exists a bijection mapping X to a proper subset of X.
>
> Equivalently and much easier to work with, a set X is said to be infinite if and only if there exists an injective but non-surjective function mapping X to itself.
>
> Here I formally prove this equivalency using my DC Proof 2.0 freeware:
>
> http://dcproof.com/DedekindEquivalentDefinitions.htm (361 lines)
>
> From set theory, it makes use of only axioms for subsets, Cartesian products and functions. I make no use of any form of AC.
>
> For an intuitive, non-numerical development of the definitions of finite and infinite see my blog posting at https://dcproof.wordpress.com/2014/09/17/infinity-the-story-so-far/
>
> Dan
>
> Download my DC Proof 2.0 freeware at http://www.dcproof.com
> Visit my Math Blog at http://www.dcproof.wordpress.com

You did quite quickly a long proof, 361 lines.

So, today was your lucky day?

Did you use some existing proof somewhere?

Mostowski Collapse schrieb am Samstag, 5. Juni 2021 um 23:04:41 UTC+2:
> Ok, I see, some progress.
>
> Pitty its not FOL+ZFC, but you HOL.
> Dan Christensen schrieb am Samstag, 5. Juni 2021 um 19:51:08 UTC+2:
> > From Richard Dedekind, a set X is said to be infinite if and only if there exists a bijection mapping X to a proper subset of X.
> >
> > Equivalently and much easier to work with, a set X is said to be infinite if and only if there exists an injective but non-surjective function mapping X to itself.
> >
> > Here I formally prove this equivalency using my DC Proof 2.0 freeware:
> >
> > http://dcproof.com/DedekindEquivalentDefinitions.htm (361 lines)
> >
> > From set theory, it makes use of only axioms for subsets, Cartesian products and functions. I make no use of any form of AC.
> >
> > For an intuitive, non-numerical development of the definitions of finite and infinite see my blog posting at https://dcproof.wordpress.com/2014/09/17/infinity-the-story-so-far/
> >
> > Dan
> >
> > Download my DC Proof 2.0 freeware at http://www.dcproof.com
> > Visit my Math Blog at http://www.dcproof.wordpress.com

On Saturday, June 5, 2021 at 5:08:20 PM UTC-4, Mostowski Collapse wrote:

> > Dan Christensen schrieb am Samstag, 5. Juni 2021 um 19:51:08 UTC+2:
> > > From Richard Dedekind, a set X is said to be infinite if and only if there exists a bijection mapping X to a proper subset of X.
> > >
> > > Equivalently and much easier to work with, a set X is said to be infinite if and only if there exists an injective but non-surjective function mapping X to itself.
> > >
> > > Here I formally prove this equivalency using my DC Proof 2.0 freeware:
> > >
> > > http://dcproof.com/DedekindEquivalentDefinitions.htm (361 lines)
> > >
> > > From set theory, it makes use of only axioms for subsets, Cartesian products and functions. I make no use of any form of AC.
> > >
> > > For an intuitive, non-numerical development of the definitions of finite and infinite see my blog posting at https://dcproof.wordpress.com/2014/09/17/infinity-the-story-so-far/
> > >

> You did quite quickly a long proof, 361 lines.
>
> So, today was your lucky day?
>
> Did you use some existing proof somewhere?

In each half of the proof, I proved the existence of the required function g.

Dan

Download my DC Proof 2.0 freeware at http://www.dcproof.com
Visit my Math Blog at http://www.dcproof.wordpress.com

Why mindless fools of logic Christensen & Burse, never recognize they have to fix Boole first, before going forward

n) AP's 174th book// Mathopedia-- Listing of 67 fakes and mistakes of Old Math.

Last revision was 16May2021.

Preface: I suppose, going forward, mathematics should always have a mathopedia, where major parts of mathematics as a science are held under question as to correctness. In past history we have called these incidents as "doubters of the mainstream". Yet math, like physics, can have no permanent mainstream, since there is always question of correctness in physics, there then corresponds question of correctness in mathematics (because math is a subset of physics). What I mean is that each future generation corrects some mistakes of past mathematics. If anyone is unsure of what I am saying here, both math and physics need constant correcting, never belonged in science. This then converges with the logic-philosophy of Pragmatism (see AP's book of logic on Pragmatism).

Some of these can be found in AP's TEACHING TRUE MATHEMATICS series, but the entries keep changing and added on new, means I need to have a separate book for these fakes, mistakes and errors of Old Math.

TEACHING TRUE MATHEMATICS: Volume 3 for ages 18-19 Freshperson College, math textbook series, book 3
Teaching True Mathematics, by Archimedes Plutonium 2019
Listing the Errors of Old Math, list of 1 to 50.

Alright, well, mathematics is a closed subject. What I mean by that is due to the textbook series of Archimedes Plutonium TEACHING TRUE MATHEMATICS, that once you learn the polynomial transform and learn the two Power Rules of Calculus, you reached the peak, the pinnacle of all of mathematics, and anything further in math is just details of what you learn in that textbook series. Math is a completed science, unlike the other 5 hard sciences of physics, chemistry, biology, geology, astronomy. Those other five will continue to find new ideas, new things, while math remains static and complete. Mathematics is finished complete as far as a science goes. And even though Physics will find new science such as how the proton toruses inside of atoms are configured in geometry, the geometry and calculus used in that configuration, that new science does not change nor does it create or require new math to handle the new physics.

Now I do need to discuss the Errors of Math in General and the errors of math in geometry in particular. I have the feeling that Geometry is the more important of the two-- algebra - geometry. This list appears in most of AP's Teaching True Mathematics textbook series by Archimedes Plutonium, meant to be a guide and orientation, and a organizing of what must be covered before graduating from College, and what math to steer clear of.

Errors mostly, but not always, for some are included because too much time spent on them.

The listings in Mathopedia of errors, mistakes and fakes is based on the idea that Calculus is the supreme achievement of all of mathematics for it is the essential math of doing Physics electricity and magnetism. And in order to have a proof of the Fundamental Theorem of Calculus, we must clean up and clean out all the mistakes, fakes and errors of Old Math, erst, we have no Calculus. So calculus is the consistency maker for the rest of all of mathematics.

1) Calculus requires a geometry proof of Fundamental Theorem of Calculus, a proof that derivative and integral are inverses of one another, just as addition and subtraction are inverses, or, multiplication and division are inverses. The only way to obtain a geometry proof is to clean up and clean out all the fakes, mistakes and errors of Old Math, such as their fake numbers-- the Reals. Their fake definition of function allowing anything be a function. Their fakery of a continuum when even physics by 1900 with Planck onwards in Quantum Mechanics proving the Universe is discrete Space not a continuum, yet by 1900 onwards those in mathematics following the idiotic continuum in the Continuum Hypothesis with even more avid interest, when they should have thrown the continuum on a trashpile of shame.

2) The true numbers of mathematics are the Decimal Grid Numbers, because you have to need and apply one mechanism only to obtain the true numbers of mathematics-- Mathematical Induction. In Old Math they had just a tiny few intelligent mathematicians, Kronecker, who emerged from the gaggle crowd of kooks to notice that Naturals all come from one single mechanism-- Mathematical Induction. But Old Math never had a crowd of mathematicians with logical brains to say-- all our numbers need to come from the one mechanism of Mathematical Induction.

3) The true numbers of math have empty space between successor and predecessor numbers. For example the 10 Grid is 0, .1, .2, .3, . . . , 9.8, 9.9, 10..0. Where no numbers exist between .1 and .2, etc. Only discrete numbers allow us to give a proof of Fundamental Theorem of Calculus.

4) All functions of mathematics must be a polynomial, and if not a polynomial, convert the offering to a polynomial over a specific interval.

5) Space is discrete and all lines in space are strings of attached straight lines.

6) No curves exist in Geometry, only finer and smaller straight line segments attached to one another.
We can still keep the name "curve" as long as we know it is a string of fine tiny straightline segments strung together in what looks like a smooth curve. If curves exist, then the Calculus in Fundamental Theorem of Calculus cannot be proven and thus Calculus does not exist. We all know that we have to have Calculus, and so we throw out onto the trash pile the curve of Old Math. And this is reasonable because starting in 1900 in physics there arose the Quantum Mechanics of Space being discrete. And a discrete space has no continuum, has no curve of Old Math.

7) Space has gaps in between one point and the next point. These gaps are empty space from one point to the next point, for example in 10 Grid there is no number between .1 and .2, and in 100 Grid there exists no number between .01 and .02.

8) Limit analysis was an insane fakery in Old Math, concocted because Old Math needed the excuse of some proof, so they invented the monster con-artist trick that a limit analysis would divert the fact it is no proof at all, but a Non Sequitur argument. Limit analysis is juju totem witchcraft dance around a desire to prove the Fundamental Theorem of Calculus. Just as idiotic as dancing around a sick person of a virus is going to cure the person.

9) Infinity has a borderline and there is a microinfinity compared to a macroinfinity. For example in 10 Grid, the microinfinity is .1 if we exclude 0 and so there is no number smaller than .1 and no number larger than 10 in 10 Grid, where 10 is macroinfinity.

10) The 1st Quadrant Only in Coordinate System Geometry. Sad that the first coordinate system of Descartes was correct but soon became corrupted with 4 quadrants. See Mathematical Thought, Volume 1, Kline, 1972, page 303. Where Fermat then Descartes starts the Cartesian Coordinate System as 1 axis only and from 0 rightwards, meaning in our modern day math, 1st Quadrant Only. Why did math screw up on coordinate systems? I suppose some clowns thought negative numbers were true and they wanted ease of drawing a circle with center at 0. When they could have just as easily drawn the circle in 1st Quadrant Only.

11) Calculus needed a Geometry proof of the Fundamental Theorem of Calculus, but Old Math never provided such, instead they provided some stupid Limit argument. The reason for the creation of the Limit disaster was that the French mathematician Cauchy got sick and tired of hearing his smartest students complain that the width of rectangles in the integral are 0 width, and those smart students could not, for the life of them understand how a rectangle with 0 width has any interior area. So instead of the math community denouncing the limit, instead they elevated the fakery.

12) Further in Calculus, they knew you could do a transform of coordinate points to turn any function into a polynomial function, a method of Lagrange.. However, they in Old Math were too stupid to take this transform to its highest form-- all functions are polynomial functions and only polynomial functions. When you learn that-- the derivative and integral of any and every function of math is a snap breeze simple and easy.

13) With the error filled 4 quadrants, when it should be 1st Quadrant Only, we have Trigonometry's sine and cosine with the fakery of sinusoid wave when it never was that. The sine and cosine are semicircle waves, and no sinusoid wave exists.

14) There is only one Geometry-- Euclidean, and there is not three distinct geometries of elliptical Riemannian or hyperbolic Lobachevsky. Those two are just duals that make up Euclidean.

15) Torus, volume and surface area formulas in Old Math are all screwed up and in error because they imagined bending a cylinder to form a torus. This brings back memories, for I had to do a percentage formula, since I could not follow the fake way of bending a cylinder. Where 78.5% of Disc Torus (pi)R^2h - (pi)r^2h is the volume of Circle Torus, and 78.5% of Disc Torus 2(pi)Rh + 2(pi)rh + 2 ((pi)R^2 - (pi)r^2) is the surface area of Circle Torus..

16) Ellipse is never a single cone slant cut, always a cylinder slant cut. Although you do get an ellipse from double cones of this configuration <> which in Old Math was the hyperbola, but two hyperbolas joined together to form a ellipse.

17) All Parallelepipeds reduced to a Rectangular Box by making 2 cuts and pastes. Volume of the original Parallelepiped is simply a*b*c of the Rectangular Box length*width*depth formed. Old Math never understood that a precise definition of Parallelepiped has two kinds, the parallelepiped that has 90 degree angles and the parallelepiped that has no 90 degree angle.

Click here to read the complete article

Parallel lines never meet, unless you bend one or both of them.

tech / sci.math / Equivalent definition of Dedekind-infinite sets

Subject	Author
Equivalent definition of Dedekind-infinite sets	Dan Christensen
Dan Christensen fixing the Google search bias of Terence Tao & Andrew	Archimedes Plutonium
WARNING TO STUDENTS: Don't be a victim of AP's fake math and science	Dan Christensen
Re: Equivalent definition of Dedekind-infinite sets	Mostowski Collapse
Re: Equivalent definition of Dedekind-infinite sets	Mostowski Collapse
Re: Equivalent definition of Dedekind-infinite sets	Dan Christensen
Mindless morons of logic-- Dan Christensen, Jan Burse, cannot even	Archimedes Plutonium
Re: Archimedes "moron of logic" Plutonium flunked the math test of a	Michael Moroney
Re: Mindless morons of logic-- Dan Christensen, Jan Burse, cannot	Dan Christensen