You can teach a mule to go to water, but you have a harder time of teaching two arsewipes of Jan Burse & Dan Christensen to post their bullshit to sci..logic.

Jan Burse is a failure of logic.

Dan Christensen is a worse failure of logic.

Hard to penetrate their mindless airhead skulls, and there is only air up there.

This is where the education system at Canadian University of Western Ontario and ETH Zurich failed all of us, in that they encourage the mindless spamming behavior of Jan Burse and Dan Christensen.

So let us ask the professors of ETH-Zurich and Univ Western Ontario why they allow and encourage spamming of bullshit to sci.math. If they went exclusively to sci.logic, no-one would say a word. But no, idiots want the spotlight in sci.math, the glitz and glamour of being near the King of Science. Thinking the King is going to throw them a morsel or two. Just the opposite, the King wants them out of sci.math. For the insanity of Burse and Christensen only attract more insane nuts.

> ETH Zurich
>
> Paul Biran, Marc Burger, Patrick Cheridito, Manfred Einsiedler, Paul Embrechts
> Giovanni Felder, Alessio Figalli, Norbert Hungerbuhler, Tom Ilmanen, Horst Knorrer
> Emmanuel Kowalski
> Urs Lang
> Rahul Pandharipande
> Richard Pink
> Tristan Riviere
> Dietmar Salamon
> Martin Schweizer
> Mete Soner
> Michael Struwe
> Benjamin Sudakov
> Alain Sznitman
> Josef Teichmann
> Wendelin Werner
> Thomas Willwacher
>
> Zurich ETH, physics dept
> Charalampos Anastasiou, Niklas Beisert, Adrian Biland, Gianni Blatter, Marcella Carollo, Christian Degen, Leonardo Degiorgi, Gunther Dissertori, Klaus Ensslin, Tilman Esslinger, Jerome Faist, Matthias Gaberdiel, Aude Gehrmann-De Ridder, Vadim Geshkenbein, Christophorus Grab, Michele Graf, Jonathan Home, Roland Horisberger, Sebastian Huber, Thomas Markus Ihn, Atac Imamoglu, Steven Johnson, Ursula Keller, Klaus Kirch, Simon Lilly, Joel Mesot, Renatto Renner, Andre Rubbia, Werner Schmutz, Thomas Schulthess, Manfred Sigrist, Hans-Arno Synal, Matthias Troyer, Andreas Vaterlaus, Rainer Wallny, Andreas Wallraff, Werner Wegscheider, Audrey Zheludev, Oded Zilberberg
>
>
> University Bern
> Christian Leumann
> Walter Benjamin
> Emil Theodor Kocher
> Kurt Wuthrich
> Daniel Vassella
> Rene Fasel
> Mani Matter
>

Univ Western Ontario math dept
Janusz Adamus, Tatyana  Barron,   Dan Christensen, Graham Denham, Ajneet Dhillon, Matthias  Franz, John Jardine, Massoud Khalkhali, Nicole Lemire, Jan Mináč, Victoria Olds, Martin Pinsonnault, Lex Renner, David Riley, Rasul Shafikov, Gordon Sinnamon

Chancellor Linda Hasenfratz
President Alan Shepard
Amit Chakma (chem engr)

Univ. Western Ontario physics dept
Pauline Barmby, Shantanu Basu, Peter Brown, Alex Buchel, Jan Cami, Margret Campbell-Brown, Blaine Chronik, Robert Cockcroft, John R. de Bruyn, Colin Denniston, Giovanni Fanchini, Sarah Gallagher, Lyudmila Goncharova, Wayne Hocking, Martin Houde, Jeffrey L. Hutter, Carol Jones, Stan Metchev, Silvia Mittler, Els Peeters, Robert Sica, Aaron Sigut, Peter Simpson, Mahi Singh, Paul Wiegert, Eugene Wong, Martin Zinke-Allmang

On Monday, October 21, 2019 at 1:29:49 PM UTC-5, Dan Christensen wrote:
>
> Are you ready, kids??? Bend over, er...
>
> Dan

Re: 81,045-Student victims of Rose M. Patten Univ Toronto from stalker Dan Christensen teaching 10 OR 2 = 12 with AND as subtraction, never a geometry proof of Fundamental Theorem of Calculus Univ Toronto, physics, Gordon F.. West, Michael B. Walker
by Frank Cassa 12Apr2021 7:00 AM 

Re: 7,744-Student victims of Linda Hasenfratz Univ Western Ontario from stalker Dan Christensen teaching 10 OR 2 = 12 with AND as subtraction, never a geometry proof of Fundamental Theorem of Calculus Chancellor Linda Hasenfratz President Alan Shepard
11:53 AM 10Apr2021
by Wayne Decarlo

Re: 102,852-Student victims of Dominic Barton, Univ Waterloo from stalker Dan Christensen teaching 10 OR 2 = 12 with AND as subtraction, never a geometry proof of Fundamental Theorem of Calculus Dominic Barton, President Feridun Hamdullahpur physics
by konyberg Apr 15, 2021, 3:09:41 PM 

Re: 176,232-Student Victims of Michael Meighen McGill Univ by Dan Christensen teaching 10 OR 2 = 12 with AND as subtraction, never a geometry proof of Fundamental Theorem of Calculus... 0.5MeV electron when in truth it is the muon as the real electron
by Dan Christensen Jul 2, 2021, 9:47:42 AM

Re: 135,568 Student victims Queen's Univ. James Leech, Arthur B. McDonald by Dan Christensen teaching 10 OR 2 = 12 with AND as subtraction, never a geometry proof of Fundamental Theorem of Calculus-- his mindless electron =0.5MeV when real electron of
May 10, 2021
by Professor Wordsmith

Re: 135,566 Student victims Queen's Univ. James Leech, Arthur B. McDonald by Dan Christensen teaching 10 OR 2 = 12 with AND as subtraction, never a geometry proof of Fundamental Theorem of Calculus-- his mindless electron =0.5MeV when real electron o
May 10, 2021
by Michael Moroney

Re: Proof of Kepler Packing//Jan Burse-Alzheimer faggot//ETH Zurich, Dietmar Salamon, Martin Schweizer, Mete Soner, looking at it
by Dan Christensen Jul 9, 2017, 11:34:05 PM

Re: *Fire the entire Univ Western Ontario math dept/ still teaching that the contradictory sine graph as sinusoid when it is really semicircle
by Dan Christensen Nov 21, 2017,

Re: Shit for brains in Logic Morons of logic George Boole, William Jevons, Bertrand Russell, Kurt Godel, Rudolf Carnap, Jan Burse& Dan Christensen as moronette cadets of Boole, Ludwig Wittgenstein, Willard Quine, Alfred North Whitehead, Irving Copi
by zelos...@gmail.com Mar 25, 2021, 12:55:15 AM 

Re: Spamming fuckdog Dan Christensen says fire Stanford's John Lipa, Alexander Fetter, William Little, Douglas Osheroff, David Ritson, H. Alan Schwettman, John Turneaure, Robert Wagoner, Stanley Wojcicki, Mason Yearian rather than let them brainwash our
by Mutt Buncher

                              ..
            .- " `-.   ,..-'''  ```.....'`-..
           ,      . `.'            '        `.
         .'   .' `    `           '   `..     ;
         .   ;  .'                     . `.    ;
         ;   . '                       `.  .   '
          . '                            ` `.  |
        . '.                                  '
       .          0              0            ' `.
      '                                          `
     ;                                            `
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    ;                      U                        `
    ;    ';                                         `
    :   | ;..                                 :`     `
    :    `;. ```.                           .-; |    '
    '.      `    ``..,                   .'   :'    '
     ;       `        ;'...          ..-''    '     '  I am Christensen,I am such a stupid insane imp of math and logic that I thought a vertex has a derivative, that distinct means not-distinct, and that 2 OR 1 = 3 with AND as subtraction. And I love spam reading of vvgra and tomato hello, and I am a failure of academics and so I spend most days making out hate-lists of people who actually succeed in science for my pea sized brain is envious and jealous of those who succeed in science yet I failed in science.
      `       `        ;  ````'''""'  ;      '    '
       `       `        ;            ;      '    '
        `       `        ;          ;      '    '
         `       `.       ````''''''      '    '
           `       .                     '    '
         /  `       `.                  '    '        .
        /     `       ..            ..'    .'"""""...'
       /   .`   `       ``.........-'     .'` .....'''
      / .'' ;     `                    .'   `
  ...'.'    ;    .' `                .'      `
   ""      .'  .' |    `           .; \       `
           ; .'   |      `. . . . ' .  \       `
           :'     |     '   `       ,   `.     `
                  |    '     `      '     `.    `
                  `   '       `     ;       `.  |
                  `.'          `    ;         `-'
                                `...'

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

On Monday, October 3, 2022 at 12:20:02 AM UTC-4, Archimedes Plutonium wrote:
>...Dan Christensen ...

[snip]

There you go again, Archie Poo! When will you learn? Once again...

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.

In AP's OWN WORDS here that, over the years, he has NEVER renounced or withdrawn:

“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.” (Actually 0.707)
--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]. What I like for the robots to do, is list every day, about 4 Colleges ( of the West) math dept, and ask why that math department is teaching false and fake math, and if unable to change to the correct true math, well, simply fire that math department until they can find professors who recognize truth in math from fakery...."
--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

STUDENTS BEWARE: Don't be a victim of Dan Christensen 's fake math and science
As it turns out, Dan Christensen is a complete nuthead.

Defining Undefined(f,x) as we did is perfectly fine.
Its the same situation with your definition of f1=f2 here:

1 ALL(dom):ALL(cod):ALL(f1):ALL(f2):[Set(dom) & Set(cod)
& Function(f1,dom,cod) & Function(f2,dom,cod)
=> [f1=f2 <=> ALL(a):[a ε dom => f1(a)=f2(a)]]]
Fn Equality
(From DC Spoiled in dcpsetup17.exe)

You also don't define Eq(f1,f2,dom,cod).
Whats wrong with you? Stop whining.

Dan Christensen schrieb am Montag, 3. Oktober 2022 um 06:36:33 UTC+2:
> STUDENTS BEWARE: Don't be a victim of AP's fake math and science
>
> On Monday, October 3, 2022 at 12:20:02 AM UTC-4, Archimedes Plutonium wrote:
> >...Dan Christensen ...
>
> [snip]
>
> There you go again, Archie Poo! When will you learn? Once again...
>
> 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.
>
> In AP's OWN WORDS here that, over the years, he has NEVER renounced or withdrawn:
>
> “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.” (Actually 0.707)
> --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]. What I like for the robots to do, is list every day, about 4 Colleges ( of the West) math dept, and ask why that math department is teaching false and fake math, and if unable to change to the correct true math, well, simply fire that math department until they can find professors who recognize truth in math from fakery...."
> --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

On Monday, October 3, 2022 at 2:49:01 AM UTC-4, Mostowski Collapse wrote:

> Dan Christensen schrieb am Montag, 3. Oktober 2022 um 06:36:33 UTC+2:
> > STUDENTS BEWARE: Don't be a victim of AP's fake math and science
> >
> > On Monday, October 3, 2022 at 12:20:02 AM UTC-4, Archimedes Plutonium wrote:
> > >...Dan Christensen ...
> >
> > [snip]
> >
> > There you go again, Archie Poo! When will you learn? Once again...
> >
> > 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.
> >
> > In AP's OWN WORDS here that, over the years, he has NEVER renounced or withdrawn:
> >
> > “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.” (Actually 0.707)
> > --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]. What I like for the robots to do, is list every day, about 4 Colleges ( of the West) math dept, and ask why that math department is teaching false and fake math, and if unable to change to the correct true math, well, simply fire that math department until they can find professors who recognize truth in math from fakery...."
> > --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)
> >

> STUDENTS BEWARE: Don't be a victim of Dan Christensen 's fake math and science
> As it turns out, Dan Christensen is a complete nuthead.
>

Jan Burse here (aka Mr. Collapse) comes to the defense of his fellow troll. Awwww...

> Defining Undefined(f,x) as we did is perfectly fine.

Should be "Undefined(f,dom,cod,x).

If you really think it is necessary, I recommend defining the following abbreviation:

ALL(f):ALL(dom):ALL(cod):ALL(x):[Undefined(f,dom,cod,x) <=> ALL(a):[a in f => f(a) in dom] & ~x in dom]

Where
f = function name
dom = name of domain set
cod = name of codomain set
x = name arbitrary object

For obvious reasons, Jan Burse (aka Mr. Collapse) hopes to make his "Undefined" predicate independent of the domain and range under consideration. His wonky little theorem is unprovable otherwise. Really kind of pathetic.

> Its the same situation with your definition of f1=f2 here:
>
> 1 ALL(dom):ALL(cod):ALL(f1):ALL(f2):[Set(dom) & Set(cod)
> & Function(f1,dom,cod) & Function(f2,dom,cod)
> => [f1=f2 <=> ALL(a):[a ε dom => f1(a)=f2(a)]]]
> Fn Equality
> (From DC Proof in dcpsetup17.exe)
>

As in Terence Tao's definition of function:

"Definition 3.3.7 (Equality of functions). Two functions f : X → Y, g : X → Y with the same domain and range are said to be equal, f = g [with respect to the domain X], if and only if f(x) = g(x) for all x ∈ X. (If f(x) and g(x) agree for some values of x, but not others, then we do not consider f and g to be equal.)"
--Terence Tao, "Analysis I," p. 51

(BTW that is not the latest version of DC Proof. See link.)

> You also don't define Eq(f1,f2,dom,cod).

Both of the above definitions can be used to determine whether or not functions are equal ONLY when they have the same domain and codomain. Deal with it, Jan Burse.

Dan

Download my DC Proof 2.0 freeware at http://www.dcproof.com <--- Latest version here
Visit my Math Blog at http://www.dcproof.wordpress.com

Well I prefer this definition:

ALL(f):ALL(dom):ALL(cod):[Function(f,dom,cod) => [Undefined(f,x) <=> ~x in dom]]

Why would you not use Function(_,_,_). Whats your function axiom
made for? Why replace it with nonsense like ALL(a):[a in dom => f(a) in cod]?
The longer you try to tweak a perfectly fine definition, the longer

it gets more worse. Until it is foobar, fucked up beyond recognition.

Dan Christensen schrieb am Montag, 3. Oktober 2022 um 19:10:45 UTC+2:
> If you really think it is necessary, I recommend defining the following abbreviation:
> ALL(f):ALL(dom):ALL(cod):ALL(x):[Undefined(f,dom,cod,x) <=> ALL(a):[a in f => f(a) in dom] & ~x in dom]

Corr.: I think it was this one:

ALL(h):ALL(dom):ALL(cod):[Function(f,dom,cod) => ALL(x):[Undefined(h,x) <=> ~x in dom]]

Mostowski Collapse schrieb am Dienstag, 4. Oktober 2022 um 00:58:56 UTC+2:
> Well I prefer this definition:
>
> ALL(f):ALL(dom):ALL(cod):[Function(f,dom,cod) => [Undefined(f,x) <=> ~x in dom]]
>
> Why would you not use Function(_,_,_). Whats your function axiom
> made for? Why replace it with nonsense like ALL(a):[a in dom => f(a) in cod]?
> The longer you try to tweak a perfectly fine definition, the longer
>
> it gets more worse. Until it is foobar, fucked up beyond recognition.
> Dan Christensen schrieb am Montag, 3. Oktober 2022 um 19:10:45 UTC+2:
> > If you really think it is necessary, I recommend defining the following abbreviation:
> > ALL(f):ALL(dom):ALL(cod):ALL(x):[Undefined(f,dom,cod,x) <=> ALL(a):[a in f => f(a) in dom] & ~x in dom]

See my reply just now to your identical posting at sci.logic.

Dan

On Monday, October 3, 2022 at 6:58:56 PM UTC-4, Mostowski Collapse wrote:
> Well I prefer this definition:
>
> ALL(f):ALL(dom):ALL(cod):[Function(f,dom,cod) => [Undefined(f,x) <=> ~x in dom]]
>
> Why would you not use Function(_,_,_). Whats your function axiom
> made for? Why replace it with nonsense like ALL(a):[a in dom => f(a) in cod]?
> The longer you try to tweak a perfectly fine definition, the longer
>
> it gets more worse. Until it is foobar, fucked up beyond recognition.
> Dan Christensen schrieb am Montag, 3. Oktober 2022 um 19:10:45 UTC+2:
> > If you really think it is necessary, I recommend defining the following abbreviation:
> > ALL(f):ALL(dom):ALL(cod):ALL(x):[Undefined(f,dom,cod,x) <=> ALL(a):[a in f => f(a) in dom] & ~x in dom]

On Monday, October 3, 2022 at 1:10:45 PM UTC-4, Dan Christensen wrote:
> On Monday, October 3, 2022 at 2:49:01 AM UTC-4, Mostowski Collapse wrote:
>
> > Dan Christensen schrieb am Montag, 3. Oktober 2022 um 06:36:33 UTC+2:
> > > STUDENTS BEWARE: Don't be a victim of AP's fake math and science
> > >
> > > On Monday, October 3, 2022 at 12:20:02 AM UTC-4, Archimedes Plutonium wrote:
> > > >...Dan Christensen ...
> > >
> > > [snip]
> > >
> > > There you go again, Archie Poo! When will you learn? Once again...
> > >
> > > 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.
> > >
> > > In AP's OWN WORDS here that, over the years, he has NEVER renounced or withdrawn:
> > >
> > > “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.” (Actually 0.707)
> > > --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]. What I like for the robots to do, is list every day, about 4 Colleges ( of the West) math dept, and ask why that math department is teaching false and fake math, and if unable to change to the correct true math, well, simply fire that math department until they can find professors who recognize truth in math from fakery...."
> > > --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)
> > >
> > STUDENTS BEWARE: Don't be a victim of Dan Christensen 's fake math and science
> > As it turns out, Dan Christensen is a complete nuthead.
> >
> Jan Burse here (aka Mr. Collapse) comes to the defense of his fellow troll. Awwww...
> > Defining Undefined(f,x) as we did is perfectly fine.
> Should be "Undefined(f,dom,cod,x).
>
> If you really think it is necessary, I recommend defining the following abbreviation:
>
> ALL(f):ALL(dom):ALL(cod):ALL(x):[Undefined(f,dom,cod,x) <=> ALL(a):[a in f => f(a) in dom] & ~x in dom]
>

Should be: ALL(f):ALL(dom):ALL(cod):ALL(x):[Undefined(f,dom,cod,x) <=> ALL(a):[a in dom => f(a) in cod] & ~x in dom]

> Where
> f = function name
> dom = name of domain set
> cod = name of codomain set
> x = name arbitrary object
>
> For obvious reasons, Jan Burse (aka Mr. Collapse) hopes to make his "Undefined" predicate independent of the domain and range under consideration. His wonky little theorem is unprovable otherwise. Really kind of pathetic.
> > Its the same situation with your definition of f1=f2 here:
> >
> > 1 ALL(dom):ALL(cod):ALL(f1):ALL(f2):[Set(dom) & Set(cod)
> > & Function(f1,dom,cod) & Function(f2,dom,cod)
> > => [f1=f2 <=> ALL(a):[a ε dom => f1(a)=f2(a)]]]
> > Fn Equality
> > (From DC Proof in dcpsetup17.exe)
> >
>
> As in Terence Tao's definition of function:
>
> "Definition 3.3.7 (Equality of functions). Two functions f : X → Y, g : X → Y with the same domain and range are said to be equal, f = g [with respect to the domain X], if and only if f(x) = g(x) for all x ∈ X. (If f(x) and g(x) agree for some values of x, but not others, then we do not consider f and g to be equal.)"
> --Terence Tao, "Analysis I," p. 51
>
> (BTW that is not the latest version of DC Proof. See link.)
> > You also don't define Eq(f1,f2,dom,cod).
> Both of the above definitions can be used to determine whether or not functions are equal ONLY when they have the same domain and codomain. Deal with it, Jan Burse.
>
> Dan
>
> Download my DC Proof 2.0 freeware at http://www.dcproof.com <--- Latest version here
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