On 11/6/2023 5:00 AM, Adam Polak wrote:
Dear Friends,
The Set Theory, creator of which is considered to be Professor Georg
Cantor, currently adhered to by the vast majority of scientists, is an
undoubtedly flawed theory, based on erroneous assumptions and, as a
result, filled with errors and internal contradictions.
So I see you never got this memo: https://en.wikipedia.org/wiki/Zermelo%E2%80%93Fraenkel_set_theory
*Cantor's set theory has been called naive set theory for a long time*
*I am surprised that no one here seemed to know this and the above* https://en.wikipedia.org/wiki/Naive_set_theory
On Wednesday, November 22, 2023 at 1:47:36 AM UTC+1, olcott wrote:
*I am surprised that no one here seemed to know this and the above*
https://en.wikipedia.org/wiki/Naive_set_theory
That's because we don't know any set theory (naive and/or axiomatic).
On 11/21/2023 6:37 PM, olcott wrote:
On 11/6/2023 5:00 AM, Adam Polak wrote:
Dear Friends,
The Set Theory, creator of which is considered to be Professor Georg
Cantor, currently adhered to by the vast majority of scientists, is an
undoubtedly flawed theory, based on erroneous assumptions and, as a
result, filled with errors and internal contradictions.
So I see you never got this memo:
https://en.wikipedia.org/wiki/Zermelo%E2%80%93Fraenkel_set_theory
*Cantor's set theory has been called naive set theory for a long time*
*I am surprised that no one here seemed to know this and the above* https://en.wikipedia.org/wiki/Naive_set_theory
On 11/21/2023 6:37 PM, olcott wrote:
On 11/6/2023 5:00 AM, Adam Polak wrote:
Dear Friends,
The Set Theory, creator of which is considered to be Professor Georg
Cantor, currently adhered to by the vast majority of scientists, is an
undoubtedly flawed theory, based on erroneous assumptions and, as a
result, filled with errors and internal contradictions.
So I see you never got this memo: https://en.wikipedia.org/wiki/Zermelo%E2%80%93Fraenkel_set_theory
*Cantor's set theory has been called naive set theory for a long time*
*I am surprised that no one here seemed to know this and the above* https://en.wikipedia.org/wiki/Naive_set_theory
--
Copyright 2023 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer
olcott explained on 11/21/2023 :
On 11/21/2023 6:37 PM, olcott wrote:
On 11/6/2023 5:00 AM, Adam Polak wrote:
Dear Friends,
The Set Theory, creator of which is considered to be Professor Georg
Cantor, currently adhered to by the vast majority of scientists, is
an undoubtedly flawed theory, based on erroneous assumptions and, as
a result, filled with errors and internal contradictions.
So I see you never got this memo:
https://en.wikipedia.org/wiki/Zermelo%E2%80%93Fraenkel_set_theory
*Cantor's set theory has been called naive set theory for a long time*
*I am surprised that no one here seemed to know this and the above*
https://en.wikipedia.org/wiki/Naive_set_theory
You assume too much with so little evidence. Maybe we seem not to know because we mostly tend to ignore the obvious trolls and cranks.
Dear Friends,contradictions.
The Set Theory, creator of which is considered to be Professor Georg Cantor, currently adhered to by the vast majority of scientists, is an undoubtedly flawed theory, based on erroneous assumptions and, as a result, filled with errors and internal
The wide "Analysis of mistakes in infinity study attempts" within set theory can be found here on YouTube:
https://www.youtube.com/watch?v=s23Cz8A0BKs
In the upcoming presentations, we will together take a colser look on numerous errors in set theory, we will identify Hilbert's Grand Hotel Paradox errors, easily solve the Continuum Hypothesis (allegedly undecidable),
and we will confirm even more emphatically that the set theory can be seen only as erroneous and disproven.
A small sample below. A comparison that decisively, in an unquestionable manner, refutes the Cantor's Diagonal Argument as evidence of the inequality of the infinite set of real numbers relative to the infinite set of natural numbers.
A hotel with an infinite number of rooms.
There is a guest in each room.
As a result, you have two infinite sets:
An infinite SET OF ROOMS containing elements with the following symbols: R1, R2, R3, ...
An infinite SET OF GUEST containing elements with the following symbols: G1, G2, G3...
A new guest appears: NG1
The new guest is definitely not among the guests that are already in the hotel because he is different from them, his name is: ("NG" + its individual number ) , everyone present in the hotel is: ("G"+ individual number of each ).
If you claim that you can accommodate a new guest in room 1 and move everyone currently present in the hotel to rooms n+1
you can do exactly the same thing with a "new" real number supposedly created by diagonal method.
You assign "new" real numb to 1, and you shift all the real numbers previously in the right column of the diagonal matrix down by one: the one that was assigned to 1 is now assigned to 2, the one assigned to 2 is now assigned to 3, etc.
It is mutually contradictory to say that you can accommodate a new guest in Hilbert's hotel and at the same time to say that you cannot find a natural number as a pair for a "new" real number "created" by the diagonal method.
The set theory is clearly contradictory in many places.
Best Regards,
Adam Polak
Russell's Paradox, the Paradox of the set of all sets,
These two have been abolished by (axiomatic set theory) https://en.wikipedia.org/wiki/Zermelo%E2%80%93Fraenkel_set_theory
a very long time ago.
On Wednesday, November 22, 2023 at 11:31:32 PM UTC+1, olcott wrote:
Russell's Paradox, the Paradox of the set of all sets,
These two have been abolished by (axiomatic set theory)
https://en.wikipedia.org/wiki/Zermelo%E2%80%93Fraenkel_set_theory
a very long time ago.
Though there are axiomatic set theories which do allow for a set of all sets.
This set does not necessarily lead to a set theoretic antinomy (though "the Russell set" does and always will do so).
Of course, if V is the set of all sets then V e V. (Still no problem in an appropriate axiomatic set theory).
In the context of ZF(C), of course, there's no such set.
On 11/22/2023 5:18 PM, Fritz Feldhase wrote:
On Wednesday, November 22, 2023 at 11:31:32 PM UTC+1, olcott wrote:
Russell's Paradox, the Paradox of the set of all sets,
These two have been abolished by (axiomatic set theory)
https://en.wikipedia.org/wiki/Zermelo%E2%80%93Fraenkel_set_theory
a very long time ago.
Though there are axiomatic set theories which do allow for a set of all sets.
This set does not necessarily lead to a set theoretic antinomy (though "the Russell set" does and always will do so).
Of course, if V is the set of all sets then V e V. (Still no problem in an appropriate axiomatic set theory).
In the context of ZF(C), of course, there's no such set.My key unique innovation to this is that a set that contains itself
is isomorphic to a can of soup that contains itself such that this can
of soup has no outside surface.
So we simply must forbid a set from containing itself as incoherent.
--
Copyright 2023 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer
On 11/22/2023 5:18 PM, Fritz Feldhase wrote:
On Wednesday, November 22, 2023 at 11:31:32 PM UTC+1, olcott wrote:
Russell's Paradox, the Paradox of the set of all sets,
These two have been abolished by (axiomatic set theory)
https://en.wikipedia.org/wiki/Zermelo%E2%80%93Fraenkel_set_theory
a very long time ago.
Though there are axiomatic set theories which do allow for a set of all sets.
This set does not necessarily lead to a set theoretic antinomy (though "the Russell set" does and always will do so).
Of course, if V is the set of all sets then V e V. (Still no problem in an appropriate axiomatic set theory).
In the context of ZF(C), of course, there's no such set.My key unique innovation to this is that a set that contains itself
is isomorphic to a can of soup that contains itself such that this can
of soup has no outside surface.
So we simply must forbid a set from containing itself as incoherent.
--
Copyright 2023 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer
czwartek, 23 listopada 2023 o 02:58:10 UTC+1 olcott napisał(a):
On 11/22/2023 5:18 PM, Fritz Feldhase wrote:
On Wednesday, November 22, 2023 at 11:31:32 PM UTC+1, olcott wrote:My key unique innovation to this is that a set that contains itself
Russell's Paradox, the Paradox of the set of all sets,
These two have been abolished by (axiomatic set theory)
https://en.wikipedia.org/wiki/Zermelo%E2%80%93Fraenkel_set_theory
a very long time ago.
Though there are axiomatic set theories which do allow for a set of all sets.
This set does not necessarily lead to a set theoretic antinomy (though "the Russell set" does and always will do so).
Of course, if V is the set of all sets then V e V. (Still no problem in an appropriate axiomatic set theory).
In the context of ZF(C), of course, there's no such set.
is isomorphic to a can of soup that contains itself such that this can
of soup has no outside surface.
So we simply must forbid a set from containing itself as incoherent.
--
Copyright 2023 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer
"So we simply must forbid a set from containing itself as incoherent."
So you want to forbid exactly this:
{ { } }
an empty set inserted as a single element into empty set
As you write, it is: "incoherent".
All right.
I'm glad you're in favor of debunking set theory as "incoherent".
I assure you, however, that you don't need to "forbid" anything - it's enough to show how absurd, naive and unfortunately just stupid set theory is, especially in the context of describing infinite sets.
Have a nice day :)
On 11/22/2023 11:56 PM, Adam Polak wrote:
czwartek, 23 listopada 2023 o 02:58:10 UTC+1 olcott napisał(a):
On 11/22/2023 5:18 PM, Fritz Feldhase wrote:
On Wednesday, November 22, 2023 at 11:31:32 PM UTC+1, olcott wrote: >>>My key unique innovation to this is that a set that contains itself
Russell's Paradox, the Paradox of the set of all sets,
These two have been abolished by (axiomatic set theory)
https://en.wikipedia.org/wiki/Zermelo%E2%80%93Fraenkel_set_theory
a very long time ago.
Though there are axiomatic set theories which do allow for a set of all sets.
This set does not necessarily lead to a set theoretic antinomy (though "the Russell set" does and always will do so).
Of course, if V is the set of all sets then V e V. (Still no problem in an appropriate axiomatic set theory).
In the context of ZF(C), of course, there's no such set.
is isomorphic to a can of soup that contains itself such that this can
of soup has no outside surface.
So we simply must forbid a set from containing itself as incoherent.
--
Copyright 2023 Olcott "Talent hits a target no one else can hit; Genius >> hits a target no one else can see." Arthur Schopenhauer
"So we simply must forbid a set from containing itself as incoherent."
Did you know that ZFC already does forbid this?
So you want to forbid exactly this:--
{ { } }
an empty set inserted as a single element into empty set
As you write, it is: "incoherent".
All right.
I'm glad you're in favor of debunking set theory as "incoherent".
I assure you, however, that you don't need to "forbid" anything - it's enough to show how absurd, naive and unfortunately just stupid set theory is, especially in the context of describing infinite sets.
Have a nice day :)
Copyright 2023 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer
On 11/22/2023 5:18 PM, Fritz Feldhase wrote:
On Wednesday, November 22, 2023 at 11:31:32 PM UTC+1, olcott wrote:
Russell's Paradox, the Paradox of the set of all sets,
These two have been abolished by (axiomatic set theory)
https://en.wikipedia.org/wiki/Zermelo%E2%80%93Fraenkel_set_theory
a very long time ago.
Though there are axiomatic set theories which do allow for a set of all sets.
This set does not necessarily lead to a set theoretic antinomy (though "the Russell set" does and always will do so).
Of course, if V is the set of all sets then V e V. (Still no problem in an appropriate axiomatic set theory).
In the context of ZF(C), of course, there's no such set.
My key unique innovation to this is that a set that contains itself
is isomorphic to a can of soup that contains itself such that this can
of soup has no outside surface.
So we simply must forbid a set from containing itself as incoherent.
"So we simply must forbid a set from containing itself as incoherent."
So you want to forbid exactly this: { { } }
"ZFC already does forbid this" (olcott)
ZFC, prohibits this: { { } } ??
czwartek, 23 listopada 2023 o 02:58:10 UTC+1 olcott napisał(a):
On 11/22/2023 5:18 PM, Fritz Feldhase wrote:
On Wednesday, November 22, 2023 at 11:31:32 PM UTC+1, olcott wrote:My key unique innovation to this is that a set that contains itself
Russell's Paradox, the Paradox of the set of all sets,
These two have been abolished by (axiomatic set theory)
https://en.wikipedia.org/wiki/Zermelo%E2%80%93Fraenkel_set_theory
a very long time ago.
Though there are axiomatic set theories which do allow for a set of all
sets.
This set does not necessarily lead to a set theoretic antinomy (though "the >>> Russell set" does and always will do so).
Of course, if V is the set of all sets then V e V. (Still no problem in an >>> appropriate axiomatic set theory).
In the context of ZF(C), of course, there's no such set.
is isomorphic to a can of soup that contains itself such that this can
of soup has no outside surface.
So we simply must forbid a set from containing itself as incoherent.
--
Copyright 2023 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer
"So we simply must forbid a set from containing itself as incoherent."
So you want to forbid exactly this:
{ { } }
After serious thinking Adam Polak wrote :
czwartek, 23 listopada 2023 o 02:58:10 UTC+1 olcott napisał(a):
On 11/22/2023 5:18 PM, Fritz Feldhase wrote:
On Wednesday, November 22, 2023 at 11:31:32 PM UTC+1, olcott wrote: >>>My key unique innovation to this is that a set that contains itself
Russell's Paradox, the Paradox of the set of all sets,
These two have been abolished by (axiomatic set theory)
https://en.wikipedia.org/wiki/Zermelo%E2%80%93Fraenkel_set_theory
a very long time ago.
Though there are axiomatic set theories which do allow for a set of all >>> sets.
This set does not necessarily lead to a set theoretic antinomy (though "the
Russell set" does and always will do so).
Of course, if V is the set of all sets then V e V. (Still no problem in an
appropriate axiomatic set theory).
In the context of ZF(C), of course, there's no such set.
is isomorphic to a can of soup that contains itself such that this can
of soup has no outside surface.
So we simply must forbid a set from containing itself as incoherent.
--
Copyright 2023 Olcott "Talent hits a target no one else can hit; Genius >> hits a target no one else can see." Arthur Schopenhauer
"So we simply must forbid a set from containing itself as incoherent."
So you want to forbid exactly this:No, that is not a set containing itself.
{ { } }
Under Frege, this {1,2,3} is.
let's start with one very simple question:
how many elements does this set contain? : :
S = { 1, 3, 4/4, 18 }
{ { } } is not a set containing itself.
After serious thinking Adam Polak wrote :
czwartek, 23 listopada 2023 o 02:58:10 UTC+1 olcott napisał(a):
On 11/22/2023 5:18 PM, Fritz Feldhase wrote:
On Wednesday, November 22, 2023 at 11:31:32 PM UTC+1, olcott wrote: >>>My key unique innovation to this is that a set that contains itself
Russell's Paradox, the Paradox of the set of all sets,
These two have been abolished by (axiomatic set theory)
https://en.wikipedia.org/wiki/Zermelo%E2%80%93Fraenkel_set_theory
a very long time ago.
Though there are axiomatic set theories which do allow for a set of all >>> sets.
This set does not necessarily lead to a set theoretic antinomy (though "the
Russell set" does and always will do so).
Of course, if V is the set of all sets then V e V. (Still no problem in an
appropriate axiomatic set theory).
In the context of ZF(C), of course, there's no such set.
is isomorphic to a can of soup that contains itself such that this can
of soup has no outside surface.
So we simply must forbid a set from containing itself as incoherent.
--
Copyright 2023 Olcott "Talent hits a target no one else can hit; Genius >> hits a target no one else can see." Arthur Schopenhauer
"So we simply must forbid a set from containing itself as incoherent."
So you want to forbid exactly this:No, that is not a set containing itself.
{ { } }
Under Frege, this {1,2,3} is.
On Thursday, November 23, 2023 at 2:58:10 AM UTC+1, olcott wrote:
On 11/22/2023 5:18 PM, Fritz Feldhase wrote:
On Wednesday, November 22, 2023 at 11:31:32 PM UTC+1, olcott wrote:My key unique innovation to this is that a set that contains itself
Russell's Paradox, the Paradox of the set of all sets,
These two have been abolished by (axiomatic set theory)
https://en.wikipedia.org/wiki/Zermelo%E2%80%93Fraenkel_set_theory
a very long time ago.
Though there are axiomatic set theories which do allow for a set of all sets.
This set does not necessarily lead to a set theoretic antinomy (though "the Russell set" does and always will do so).
Of course, if V is the set of all sets then V e V. (Still no problem in an appropriate axiomatic set theory).
In the context of ZF(C), of course, there's no such set.
is isomorphic to a can of soup that contains itself such that this can
of soup has no outside surface.
So we simply must forbid a set from containing itself as incoherent.
Such a set (a hyperset) is not allowed/possible in ZF(C).
But there are variants of ZF(C) which do allow for such sets.
czwartek, 23 listopada 2023 o 11:32:25 UTC+1 FromTheRafters napisał(a):
After serious thinking Adam Polak wrote :
czwartek, 23 listopada 2023 o 02:58:10 UTC+1 olcott napisał(a):No, that is not a set containing itself.
On 11/22/2023 5:18 PM, Fritz Feldhase wrote:
On Wednesday, November 22, 2023 at 11:31:32 PM UTC+1, olcott wrote: >>>>>My key unique innovation to this is that a set that contains itself
Russell's Paradox, the Paradox of the set of all sets,
These two have been abolished by (axiomatic set theory)
https://en.wikipedia.org/wiki/Zermelo%E2%80%93Fraenkel_set_theory
a very long time ago.
Though there are axiomatic set theories which do allow for a set of all >>>>> sets.
This set does not necessarily lead to a set theoretic antinomy (though >>>>> "the Russell set" does and always will do so).
Of course, if V is the set of all sets then V e V. (Still no problem in >>>>> an appropriate axiomatic set theory).
In the context of ZF(C), of course, there's no such set.
is isomorphic to a can of soup that contains itself such that this can >>>> of soup has no outside surface.
So we simply must forbid a set from containing itself as incoherent.
--
Copyright 2023 Olcott "Talent hits a target no one else can hit; Genius >>>> hits a target no one else can see." Arthur Schopenhauer
"So we simply must forbid a set from containing itself as incoherent."
So you want to forbid exactly this:
{ { } }
Under Frege, this {1,2,3} is.
" { { } } <- No, that is not a set containing itself. "
Is that what you think? :)
let's start with one very simple question:
how many elements does this set contain? : :
{ 1, 3, 4/4, 18 }
{ 1, 3, 4/4, 18 }
Four symbols separated by three commas. I would say four elements. Cardinality four.
a set that contains itself is isomorphic to a can of soup that contains itself such that this can
of soup has no outside surface.
How about this one?
{{},elephant,gorrila,jackass}
On Thursday, November 23, 2023 at 4:59:24 PM UTC+1, FromTheRafters wrote:
{ 1, 3, 4/4, 18 }Four symbols separated by three commas. I would say four elements.
Cardinality four.
C'mon. Don't be an idiot!
Hint: If a = b = c = d, then card({a, b, c, d}) = 1.
<faceplam>
Fritz Feldhase formulated on Thursday :
On Thursday, November 23, 2023 at 4:59:24 PM UTC+1, FromTheRafters wrote:
Four symbols separated by three commas. I would say four elements.
{ 1, 3, 4/4, 18 }
Cardinality four.
C'mon. Don't be an idiot! :-)
Hint: If a = b = c = d, then card({a, b, c, d}) = 1.
Sure, but then it would not have been a set, but a multiset.
On Thursday, November 23, 2023 at 7:06:32 PM UTC+1, FromTheRafters wrote:
Fritz Feldhase formulated on Thursday :
On Thursday, November 23, 2023 at 4:59:24 PM UTC+1, FromTheRafters wrote: >>>>>Sure, but then it would not have been a set, but a multiset.
{ 1, 3, 4/4, 18 }Four symbols separated by three commas. I would say four elements.
Cardinality four.
C'mon. Don't be an idiot! :-)
Hint: If a = b = c = d, then card({a, b, c, d}) = 1.
Huh?!
Forget about it.
EOD.
Adam Polak presented the following explanation :
czwartek, 23 listopada 2023 o 11:32:25 UTC+1 FromTheRafters napisał(a):
After serious thinking Adam Polak wrote :
czwartek, 23 listopada 2023 o 02:58:10 UTC+1 olcott napisał(a):No, that is not a set containing itself.
On 11/22/2023 5:18 PM, Fritz Feldhase wrote:
On Wednesday, November 22, 2023 at 11:31:32 PM UTC+1, olcott wrote: >>>>>My key unique innovation to this is that a set that contains itself >>>> is isomorphic to a can of soup that contains itself such that this can >>>> of soup has no outside surface.
Russell's Paradox, the Paradox of the set of all sets,
These two have been abolished by (axiomatic set theory)
https://en.wikipedia.org/wiki/Zermelo%E2%80%93Fraenkel_set_theory >>>>>> a very long time ago.
Though there are axiomatic set theories which do allow for a set of all
sets.
This set does not necessarily lead to a set theoretic antinomy (though >>>>> "the Russell set" does and always will do so).
Of course, if V is the set of all sets then V e V. (Still no problem in
an appropriate axiomatic set theory).
In the context of ZF(C), of course, there's no such set.
So we simply must forbid a set from containing itself as incoherent. >>>> --
Copyright 2023 Olcott "Talent hits a target no one else can hit; Genius >>>> hits a target no one else can see." Arthur Schopenhauer
"So we simply must forbid a set from containing itself as incoherent." >>>
So you want to forbid exactly this:
{ { } }
Under Frege, this {1,2,3} is.
" { { } } <- No, that is not a set containing itself. "I know this.
Is that what you think? :)
let's start with one very simple question:Four symbols separated by three commas. I would say four elements. Cardinality four.
how many elements does this set contain? : :
{ 1, 3, 4/4, 18 }
How about this one?
{{},elephant,gorrila,jackass}
Four symbols separated by three commas. I would say four elements. Cardinality four.OK, let me ask you another question befor I'll aswer your:
Fritz Feldhase formulated on Thursday :
On Thursday, November 23, 2023 at 4:59:24 PM UTC+1, FromTheRafters wrote: >>
{ 1, 3, 4/4, 18 }Four symbols separated by three commas. I would say four elements.
Cardinality four.
C'mon. Don't be an idiot!
Hint: If a = b = c = d, then card({a, b, c, d}) = 1.
<faceplam>
Sure, but then it would not have been a set, but a multiset.
On 11/23/2023 10:06 AM, FromTheRafters wrote:
Fritz Feldhase formulated on Thursday :
On Thursday, November 23, 2023 at 4:59:24 PM UTC+1, FromTheRafters wrote: >>>
{ 1, 3, 4/4, 18 }Four symbols separated by three commas. I would say four elements.
Cardinality four.
C'mon. Don't be an idiot!
Hint: If a = b = c = d, then card({a, b, c, d}) = 1.
<faceplam>
Sure, but then it would not have been a set, but a multiset.
As a programmer, I see 4 elements. However, lets reduce and remove duplicates:
{ 1, 3, 4/4, 18 }
Can be:
{ 1, 3, 1, 18 }
Remove duplicates:
{ 1, 3, 18 }
?
czwartek, 23 listopada 2023 o 16:59:24 UTC+1 FromTheRafters napisał(a):
Adam Polak presented the following explanation :
czwartek, 23 listopada 2023 o 11:32:25 UTC+1 FromTheRafters napisał(a): >>>> After serious thinking Adam Polak wrote :Four symbols separated by three commas. I would say four elements.
czwartek, 23 listopada 2023 o 02:58:10 UTC+1 olcott napisał(a):No, that is not a set containing itself.
On 11/22/2023 5:18 PM, Fritz Feldhase wrote:
On Wednesday, November 22, 2023 at 11:31:32 PM UTC+1, olcott wrote: >>>>>>>My key unique innovation to this is that a set that contains itself >>>>>> is isomorphic to a can of soup that contains itself such that this can >>>>>> of soup has no outside surface.
Russell's Paradox, the Paradox of the set of all sets,
These two have been abolished by (axiomatic set theory)
https://en.wikipedia.org/wiki/Zermelo%E2%80%93Fraenkel_set_theory >>>>>>>> a very long time ago.
Though there are axiomatic set theories which do allow for a set of all >>>>>>> sets.
This set does not necessarily lead to a set theoretic antinomy (though >>>>>>> "the Russell set" does and always will do so).
Of course, if V is the set of all sets then V e V. (Still no problem in >>>>>>> an appropriate axiomatic set theory).
In the context of ZF(C), of course, there's no such set.
So we simply must forbid a set from containing itself as incoherent. >>>>>> --
Copyright 2023 Olcott "Talent hits a target no one else can hit; Genius >>>>>> hits a target no one else can see." Arthur Schopenhauer
"So we simply must forbid a set from containing itself as incoherent." >>>>>
So you want to forbid exactly this:
{ { } }
Under Frege, this {1,2,3} is.
" { { } } <- No, that is not a set containing itself. "
Is that what you think? :) I know this.
let's start with one very simple question:
how many elements does this set contain? : :
{ 1, 3, 4/4, 18 }
Cardinality four.
How about this one?
{{},elephant,gorrila,jackass}
Set: { 1, 3, 4/4, 18 } how many elements contain ?
Four symbols separated by three commas. I would say four elements.OK, let me ask you another question befor I'll aswer your:
Cardinality four.
Set: { 1, 3, 1.0000... , 18 } how many elements contain ?
Chris M. Thomasson submitted this idea :
On 11/23/2023 10:06 AM, FromTheRafters wrote:
Fritz Feldhase formulated on Thursday :
On Thursday, November 23, 2023 at 4:59:24 PM UTC+1, FromTheRafters
wrote:
{ 1, 3, 4/4, 18 }Four symbols separated by three commas. I would say four elements.
Cardinality four.
C'mon. Don't be an idiot!
Hint: If a = b = c = d, then card({a, b, c, d}) = 1.
<faceplam>
Sure, but then it would not have been a set, but a multiset.
As a programmer, I see 4 elements. However, lets reduce and remove
duplicates:
There are no duplicates in a ZFC set. In a multiset say:
[a,a,a,b,b,c,c,c,c]
You add the multiplicities, three a's two b's and four c's for a
cardinality of nine.
{ 1, 3, 4/4, 18 }
Can be:
{ 1, 3, 1, 18 }
Remove duplicates:
{ 1, 3, 18 }
?
A set with cardinality of three.
OK, let me ask you another question befor I'll aswer your:
Set: { 1, 3, 1.0000... , 18 } how many elements contain ?
After serious thinking Adam Polak wrote :
czwartek, 23 listopada 2023 o 16:59:24 UTC+1 FromTheRafters napisał(a):
Adam Polak presented the following explanation :
czwartek, 23 listopada 2023 o 11:32:25 UTC+1 FromTheRafters napisał(a): >>>> After serious thinking Adam Polak wrote :Four symbols separated by three commas. I would say four elements.
czwartek, 23 listopada 2023 o 02:58:10 UTC+1 olcott napisał(a): >>>>>> On 11/22/2023 5:18 PM, Fritz Feldhase wrote:No, that is not a set containing itself.
On Wednesday, November 22, 2023 at 11:31:32 PM UTC+1, olcott wrote:My key unique innovation to this is that a set that contains itself >>>>>> is isomorphic to a can of soup that contains itself such that this can
Russell's Paradox, the Paradox of the set of all sets,
These two have been abolished by (axiomatic set theory)
https://en.wikipedia.org/wiki/Zermelo%E2%80%93Fraenkel_set_theory >>>>>>>> a very long time ago.
Though there are axiomatic set theories which do allow for a set of all
sets.
This set does not necessarily lead to a set theoretic antinomy (though
"the Russell set" does and always will do so).
Of course, if V is the set of all sets then V e V. (Still no problem in
an appropriate axiomatic set theory).
In the context of ZF(C), of course, there's no such set.
of soup has no outside surface.
So we simply must forbid a set from containing itself as incoherent. >>>>>> --
Copyright 2023 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer
"So we simply must forbid a set from containing itself as incoherent." >>>>>
So you want to forbid exactly this:
{ { } }
Under Frege, this {1,2,3} is.
" { { } } <- No, that is not a set containing itself. "
Is that what you think? :) I know this.
let's start with one very simple question:
how many elements does this set contain? : :
{ 1, 3, 4/4, 18 }
Cardinality four.
How about this one?
{{},elephant,gorrila,jackass}
Set: { 1, 3, 4/4, 18 } how many elements contain ?A four element multiset.
Four symbols separated by three commas. I would say four elements.OK, let me ask you another question befor I'll aswer your:
Cardinality four.
Set: { 1, 3, 1.0000... , 18 } how many elements contain ?
Four symbols separated by three commas. I would say four elements. Cardinality four."
piątek, 24 listopada 2023 o 08:25:12 UTC+1 FromTheRafters napisał(a):
After serious thinking Adam Polak wrote :
czwartek, 23 listopada 2023 o 16:59:24 UTC+1 FromTheRafters napisał(a): >>>> Adam Polak presented the following explanation :A four element multiset.
czwartek, 23 listopada 2023 o 11:32:25 UTC+1 FromTheRafters napisał(a): >>>>>> After serious thinking Adam Polak wrote :Four symbols separated by three commas. I would say four elements.
czwartek, 23 listopada 2023 o 02:58:10 UTC+1 olcott napisał(a): >>>>>>>> On 11/22/2023 5:18 PM, Fritz Feldhase wrote:No, that is not a set containing itself.
On Wednesday, November 22, 2023 at 11:31:32 PM UTC+1, olcott wrote: >>>>>>>>>My key unique innovation to this is that a set that contains itself >>>>>>>> is isomorphic to a can of soup that contains itself such that this can >>>>>>>> of soup has no outside surface.
Russell's Paradox, the Paradox of the set of all sets,
These two have been abolished by (axiomatic set theory)
https://en.wikipedia.org/wiki/Zermelo%E2%80%93Fraenkel_set_theory >>>>>>>>>> a very long time ago.
Though there are axiomatic set theories which do allow for a set of >>>>>>>>> all sets.
This set does not necessarily lead to a set theoretic antinomy >>>>>>>>> (though "the Russell set" does and always will do so).
Of course, if V is the set of all sets then V e V. (Still no problem >>>>>>>>> in an appropriate axiomatic set theory).
In the context of ZF(C), of course, there's no such set.
So we simply must forbid a set from containing itself as incoherent. >>>>>>>> --
Copyright 2023 Olcott "Talent hits a target no one else can hit; >>>>>>>> Genius hits a target no one else can see." Arthur Schopenhauer >>>>>>>
"So we simply must forbid a set from containing itself as incoherent." >>>>>>>
So you want to forbid exactly this:
{ { } }
Under Frege, this {1,2,3} is.
" { { } } <- No, that is not a set containing itself. "
Is that what you think? :) I know this.
let's start with one very simple question:
how many elements does this set contain? : :
{ 1, 3, 4/4, 18 }
Cardinality four.
How about this one?
{{},elephant,gorrila,jackass}
Set: { 1, 3, 4/4, 18 } how many elements contain ?
Four symbols separated by three commas. I would say four elements.OK, let me ask you another question befor I'll aswer your:
Cardinality four.
Set: { 1, 3, 1.0000... , 18 } how many elements contain ?
to justify your answer: "... four elements. Cardinality four."
wrong answer in the context of the Set theory that is based on ZF(C) axiomatics, you moved to the area of "multiset" which is incompatible with ZF(C) so with the Set theory.
We learn from this that one can disagree with ZF(C) Set theory and nothing terrible happen. Good to notice.
"
Set: { 1, 3, 4/4, 18 } how many elements contain ?
Four symbols separated by three commas. I would say four elements."
Cardinality four.
what happened that you didn't recognize 4/4 as 1
as "the number ONE"
and that, in accordance with Set theory, you did not answer: three elements ? just think it over
piątek, 24 listopada 2023 o 08:25:12 UTC+1 FromTheRafters napisał(a):
After serious thinking Adam Polak wrote :
czwartek, 23 listopada 2023 o 16:59:24 UTC+1 FromTheRafters napisał(a):
Adam Polak presented the following explanation :
czwartek, 23 listopada 2023 o 11:32:25 UTC+1 FromTheRafters napisał(a):Four symbols separated by three commas. I would say four elements.
After serious thinking Adam Polak wrote :
czwartek, 23 listopada 2023 o 02:58:10 UTC+1 olcott napisał(a): >>>>>> On 11/22/2023 5:18 PM, Fritz Feldhase wrote:No, that is not a set containing itself.
On Wednesday, November 22, 2023 at 11:31:32 PM UTC+1, olcott wrote:My key unique innovation to this is that a set that contains itself >>>>>> is isomorphic to a can of soup that contains itself such that this can
Russell's Paradox, the Paradox of the set of all sets,
These two have been abolished by (axiomatic set theory)
https://en.wikipedia.org/wiki/Zermelo%E2%80%93Fraenkel_set_theory >>>>>>>> a very long time ago.
Though there are axiomatic set theories which do allow for a set of all
sets.
This set does not necessarily lead to a set theoretic antinomy (though
"the Russell set" does and always will do so).
Of course, if V is the set of all sets then V e V. (Still no problem in
an appropriate axiomatic set theory).
In the context of ZF(C), of course, there's no such set.
of soup has no outside surface.
So we simply must forbid a set from containing itself as incoherent.
--
Copyright 2023 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer
"So we simply must forbid a set from containing itself as incoherent."
So you want to forbid exactly this:
{ { } }
Under Frege, this {1,2,3} is.
" { { } } <- No, that is not a set containing itself. "
Is that what you think? :) I know this.
let's start with one very simple question:
how many elements does this set contain? : :
{ 1, 3, 4/4, 18 }
Cardinality four.
How about this one?
{{},elephant,gorrila,jackass}
to justify your answer: "... four elements. Cardinality four."Set: { 1, 3, 4/4, 18 } how many elements contain ?A four element multiset.
Four symbols separated by three commas. I would say four elements.OK, let me ask you another question befor I'll aswer your:
Cardinality four.
Set: { 1, 3, 1.0000... , 18 } how many elements contain ?
wrong answer in the context of the Set theory that is based on ZF(C) axiomatics,
you moved to the area of "multiset" which is incompatible with ZF(C) so with the Set theory.
We learn from this that one can disagree with ZF(C) Set theory and nothing terrible happen.
Good to notice.
"
Set: { 1, 3, 4/4, 18 } how many elements contain ?
Four symbols separated by three commas. I would say four elements. Cardinality four."
what happened that you didn't recognize 4/4 as 1
as "the number ONE"
and that, in accordance with Set theory, you did not answer: three elements ?
just think it over
Adam Polak wrote on 11/24/2023 :
piątek, 24 listopada 2023 o 08:25:12 UTC+1 FromTheRafters napisał(a):
After serious thinking Adam Polak wrote :
czwartek, 23 listopada 2023 o 16:59:24 UTC+1 FromTheRafters napisał(a): >>>> Adam Polak presented the following explanation :A four element multiset.
czwartek, 23 listopada 2023 o 11:32:25 UTC+1 FromTheRafters napisał(a):Four symbols separated by three commas. I would say four elements.
After serious thinking Adam Polak wrote :
czwartek, 23 listopada 2023 o 02:58:10 UTC+1 olcott napisał(a): >>>>>>>> On 11/22/2023 5:18 PM, Fritz Feldhase wrote:No, that is not a set containing itself.
On Wednesday, November 22, 2023 at 11:31:32 PM UTC+1, olcott wrote:My key unique innovation to this is that a set that contains itself >>>>>>>> is isomorphic to a can of soup that contains itself such that this can
Russell's Paradox, the Paradox of the set of all sets,
These two have been abolished by (axiomatic set theory) >>>>>>>>>> https://en.wikipedia.org/wiki/Zermelo%E2%80%93Fraenkel_set_theory >>>>>>>>>> a very long time ago.
Though there are axiomatic set theories which do allow for a set of
all sets.
This set does not necessarily lead to a set theoretic antinomy >>>>>>>>> (though "the Russell set" does and always will do so).
Of course, if V is the set of all sets then V e V. (Still no problem
in an appropriate axiomatic set theory).
In the context of ZF(C), of course, there's no such set.
of soup has no outside surface.
So we simply must forbid a set from containing itself as incoherent.
--
Copyright 2023 Olcott "Talent hits a target no one else can hit; >>>>>>>> Genius hits a target no one else can see." Arthur Schopenhauer >>>>>>>
"So we simply must forbid a set from containing itself as incoherent."
So you want to forbid exactly this:
{ { } }
Under Frege, this {1,2,3} is.
" { { } } <- No, that is not a set containing itself. "
Is that what you think? :) I know this.
let's start with one very simple question:
how many elements does this set contain? : :
{ 1, 3, 4/4, 18 }
Cardinality four.
How about this one?
{{},elephant,gorrila,jackass}
Set: { 1, 3, 4/4, 18 } how many elements contain ?
Four symbols separated by three commas. I would say four elements.OK, let me ask you another question befor I'll aswer your:
Cardinality four.
Set: { 1, 3, 1.0000... , 18 } how many elements contain ?
to justify your answer: "... four elements. Cardinality four."
wrong answer in the context of the Set theory that is based on ZF(C) axiomatics, you moved to the area of "multiset" which is incompatible with ZF(C) so with the Set theory.
We learn from this that one can disagree with ZF(C) Set theory and nothing terrible happen. Good to notice.
"I didn't recognize that collection as a set, but as a multiset, because
Set: { 1, 3, 4/4, 18 } how many elements contain ?
Four symbols separated by three commas. I would say four elements."
Cardinality four.
what happened that you didn't recognize 4/4 as 1
as "the number ONE"
ZFC sets don't have duplicate elements.
and that, in accordance with Set theory, you did not answer: three elements ?Yes, you are correct. I should have because the symbol 4/4 and the
just think it over
symbol 1 are the same number just like 1/2 and .5 and .4(9) are all the
same number.
ZFC sets don't have duplicate elements.
the symbol 4/4 and the symbol 1 are the same number just like 1/2 and .5 and .4(9) are all the same number.
Set: {1, 3, 4/4, 18} how many elements [does it] contain?
It's plenty good, and the set is unnamed too.
<psychotic bullshit deleted>
On 11/23/2023 11:23 PM, FromTheRafters wrote:
Chris M. Thomasson submitted this idea :
On 11/23/2023 10:06 AM, FromTheRafters wrote:
Fritz Feldhase formulated on Thursday :
On Thursday, November 23, 2023 at 4:59:24 PM UTC+1, FromTheRafters >>>>> wrote:
{ 1, 3, 4/4, 18 }Four symbols separated by three commas. I would say four elements. >>>>>> Cardinality four.
C'mon. Don't be an idiot!
Hint: If a = b = c = d, then card({a, b, c, d}) = 1.
<faceplam>
Sure, but then it would not have been a set, but a multiset.
As a programmer, I see 4 elements. However, lets reduce and remove
duplicates:
There are no duplicates in a ZFC set. In a multiset say:
[a,a,a,b,b,c,c,c,c]
You add the multiplicities, three a's two b's and four c's for a
cardinality of nine.
{ 1, 3, 4/4, 18 }
Can be:
{ 1, 3, 1, 18 }
Remove duplicates:
{ 1, 3, 18 }
?
A set with cardinality of three.
3-ary finite set... Fair enough?
On 11/23/2023 11:23 PM, FromTheRafters wrote:
Chris M. Thomasson submitted this idea :
On 11/23/2023 10:06 AM, FromTheRafters wrote:
Fritz Feldhase formulated on Thursday :
On Thursday, November 23, 2023 at 4:59:24 PM UTC+1, FromTheRafters >>>>> wrote:
{ 1, 3, 4/4, 18 }Four symbols separated by three commas. I would say four elements. >>>>>> Cardinality four.
C'mon. Don't be an idiot!
Hint: If a = b = c = d, then card({a, b, c, d}) = 1.
<faceplam>
Sure, but then it would not have been a set, but a multiset.
As a programmer, I see 4 elements. However, lets reduce and remove
duplicates:
There are no duplicates in a ZFC set. In a multiset say:
[a,a,a,b,b,c,c,c,c]
You add the multiplicities, three a's two b's and four c's for a
cardinality of nine.
{ 1, 3, 4/4, 18 }
Can be:
{ 1, 3, 1, 18 }
Remove duplicates:
{ 1, 3, 18 }
?
A set with cardinality of three.
3-ary finite set... Fair enough?
Neither are correct roster form set notation.
Sets don't have repeated elements.
if you remove the duplicates, it is correct roster form notation.
Neither are correct roster form set notation.
Sets don't have repeated elements.
if you remove the duplicates, it is correct roster form notation.
On Tuesday, November 28, 2023 at 7:43:16 AM UTC+1, FromTheRafters wrote:
Neither are correct roster form set notation.
Sure they are.
We (usually?) do NOT require a_i =/= a_j here for i,j e {1, ..., n}, i =/= j.
On Tuesday, November 28, 2023 at 3:56:17 PM UTC+1, Fritz Feldhase wrote:
On Tuesday, November 28, 2023 at 7:43:16 AM UTC+1, FromTheRafters wrote:
Neither are correct roster form set notation.
Sure they are.You may check this, for example: https://proofwiki.org/wiki/Existence_of_Singleton_Set
We (usually?) do NOT require a_i =/= a_j here for i,j e {1, ..., n}, i =/= j.For example:
"_Curly bracket notation_
We often define sets by listing their elements [...]:
• The symbol {x, y, z} describes the set whose elements are precisely x, y, and z."
You see, x = y = z = 1 (say) is not excluded.
[Btw. A formal version of this definition would just be: x e {a, b, c} <-> x e a v x e b v x e c.]
Source: https://math.mit.edu/~jhirsh/top_lecture.pdf
"Sure they are.You may check this, for example: https://proofwiki.org/wiki/Existence_of_Singleton_Set
On Tuesday, November 28, 2023 at 3:56:17 PM UTC+1, Fritz Feldhase wrote:
On Tuesday, November 28, 2023 at 7:43:16 AM UTC+1, FromTheRafters wrote:
Neither are correct roster form set notation.
Sure they are.You may check this, for example: https://proofwiki.org/wiki/Existence_of_Singleton_Set
We (usually?) do NOT require a_i =/= a_j here for i,j e {1, ..., n}, i =/= j.For example:
"_Curly bracket notation_
We often define sets by listing their elements [...]:
• The symbol {x, y, z} describes the set whose elements are precisely x, y, and z."
You see, x = y = z = 1 (say) is not excluded.
[Btw. A formal version of this definition would just be: x e {a, b, c} <-> x e a v x e b v x e c.]
Source: https://math.mit.edu/~jhirsh/top_lecture.pdf
"Sure they are.You may check this, for example: https://proofwiki.org/wiki/Existence_of_Singleton_Set
wtorek, 28 listopada 2023 o 16:27:59 UTC+1 Fritz Feldhase napisał(a):
On Tuesday, November 28, 2023 at 3:56:17 PM UTC+1, Fritz Feldhase wrote:
On Tuesday, November 28, 2023 at 7:43:16 AM UTC+1, FromTheRafters wrote:
Neither are correct roster form set notation.
Sure they are.You may check this, for example: https://proofwiki.org/wiki/Existence_of_Singleton_Set
We (usually?) do NOT require a_i =/= a_j here for i,j e {1, ..., n}, i =/= j.For example:
"_Curly bracket notation_
We often define sets by listing their elements [...]:
• The symbol {x, y, z} describes the set whose elements are precisely x, y, and z."
You see, x = y = z = 1 (say) is not excluded.
[Btw. A formal version of this definition would just be: x e {a, b, c} <-> x e a v x e b v x e c.]
Source: https://math.mit.edu/~jhirsh/top_lecture.pdf
"
"Sure they are.You may check this, for example: https://proofwiki.org/wiki/Existence_of_Singleton_Set
Proofs based on axioms :))
It's really amusing.
Axioms, unfortunately, being in it's important part internally contradictory, so flawed, in a way that cannot be questioned.
To say that something is true or a correct description of reality just because an axiom says so, or it follows from an axiom,
is exactly the same as saying that
God exists because it follows from the content of the Roman Catholic Church catechism.
Is it really so difficult to notice, to realize that using such methodologies of proving pushes you out from the realm of SCIENCE into the realm of an unscientific RELIGIOUS SECT?
An axiom is not an argument, much less a proof or a basis for proof!
Have a nice day.
Regards,
Adam
An axiom is not a basis for proof!
An axiom is not a basis for proof!
On Wednesday, November 29, 2023 at 9:26:50 AM UTC+1, Adam Polak wrote:thank U
Proofs based on axioms
Since you seem to like this topic:
http://de.metamath.org/
Great site.
Proofs based on axioms
środa, 29 listopada 2023 o 11:21:19 UTC+1 Fritz Feldhase napisał(a):
the step-by-step method inherently requires minimal (delta t) oneafter one, in which subsequent steps are taken.
The only type of action on the elements of an infinite series or setthat can encompass "ALL" elements of such a series or set is an action involving "ALL" elements simultaneously.
Adam Polak schrieb am Mittwoch, 29. November 2023 um 11:42:37 UTC+1:
środa, 29 listopada 2023 o 11:21:19 UTC+1 Fritz Feldhase napisał(a):Hi Adam, unfortunately your post to "A game like billiards" of today
does not appear in my news server. Therefore I answer it here:
Adam Polak schrieb am Mittwoch, 29. November 2023 um 10:34:28 UTC+1:
If the method involves STEP-by-STEP action, then the possibility of performing an action on "ALL" elements of an infinite series or set is excluded
Counting is a step-by-step procedure. _If_ Cantor is accepted, then this procedure can be completed.
the step-by-step method inherently requires minimal (delta t) oneafter one, in which subsequent steps are taken.
By using the geometric series 1 + 1/2 + 1/4 + 1/8 + ... infinitely many steps can be processed within 2 seconds.
The only type of action on the elements of an infinite series or setthat can encompass "ALL" elements of such a series or set is an action involving "ALL" elements simultaneously.
Mathematics is not time-dependent. If all steps are defined by the algorithm, and if infinitely many natural numbers can be applied at all, then this can be done like described in the OP. The only condition is
that all steps are determined and no further decisions are necessary.
wtorek, 5 grudnia 2023 o 10:42:52 UTC+1 WM napisał(a):considering bijection.
If I could suggest anything to anyone: Don't waste too much time
A necessary condition for a bijection between the elements of aninfinite set and the elements of its proper subset is that the chosen
Adam Polak wrote on 11/24/2023 :
piątek, 24 listopada 2023 o 08:25:12 UTC+1 FromTheRafters napisał(a):
"
Set: { 1, 3, 4/4, 18 } how many elements contain ?
Four symbols separated by three commas. I would say four elements."
Cardinality four.
what happened that you didn't recognize 4/4 as 1 as "the number ONE"
I didn't recognize that collection as a set, but as a multiset,
because ZFC sets don't have duplicate elements.
and that, in accordance with Set theory, you did not answer: three elements ?
just think it over
Yes, you are correct. I should have because the symbol 4/4 and the
symbol 1 are the same number just like 1/2 and .5 and .4(9) are all
the same number.
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