On Thursday, September 22, 2022 at 11:55:14 PM UTC+2, Mostowski Collapse wrote:

> Can DC Spoiled prove that this function space, where B = {0,1}:
>
> F = { f : B x B --> B }
>
> Has cardinality 16? I doubt so.

Well, we may simplify the task slightly (since DC is too dumb to deal with "cardinalities"):

Theorem:

| If B = {0, 1}, then {f | f : B x B --> B} ~ {k e IN : 0 < k <= 2^4}.

Hope that DC (and DC Spoof) can deal with 2^4, sets and bijections.

Hint@Dumbo: A ~ B means that there is a bijection from A onto B.

How about

Theorem:

| If |B| = n, then {f | f : B x B --> B} ~ {k e IN : 0 < k <= n^(n^2)}

?

Hint@Dumbo:Basic set theory, but actually quite "relevant". See: https://youtu.be/mwlMsiamS3c

On 9/23/2022 8:09 PM, Jeiker Carboni wrote:
> Michael Moroney wrote:
>
>>> hear some Russian music, I love it.
>>
>> Russian people (the un-Nazified ones, anyway) are good people with good
>> culture. Too bad Nazified 卐Russia卐 doesn't respect the Ukrainian
>> people, language and culture.
>
> there is no such thing, my friend, "uKrainian language", talking iliterate
> bad Russian is not a language.

You prove my point, nymshifter. You are going along with 卐Владольф
Путлер卐 and his would-be genocide of the Ukrainian language.

I bet the Russians could only grunt before the early Ukrainians taught
them to speak.

Should we say Spanish isn't a language because it is similar to bad
Italian? No.

> the putina didn't want to destroy the "uKraine", ie infrastructure, tv,
> radios, propaganda media etc, command centers etc, as the americans does.

Again, you prove my point about the evil of 卐Путлер卐. Kill the people,
culture language, but keep the infrastructure etc. (for the incoming
Russians). Ever hear the term "Lebensraum"? Where did that come from?
That's the same thing.

> it looks like you are the only one in nazist fascist america, not knowing
> the uKronazis are nazis.

Sorry, nymshifter. That pathetic lie won't fly. You do know Zelenskyy is
a Jew, don't you?

> let's hope the have or can make a few thousands. You khakhole americans
> can't even make a rocket motor.

Musk and his company is doing rather well doing so.
But first, let us hear about the Russian moon landings!

> The Sukhoi SU-57 stealth fighteris Russia’s answer to the West’s 5th-
> generation aircraft.

Can't wait until Ukraine shoots one down!

Why would you need classes for cardinality?
The typical text book approach bootstraps
cardinality from ordinals. You then don't

need to make a class equivalence class.
Please read this:

Basic Set Theory
Azriel Levy - 13. August 2002
https://www.amazon.com/dp/0486420795

It says "Basic", LoL.
Its very easy you define:

|A| := k <=> smallest of your ordinals k,
such that there is bijection A -> k.

your ordinal k <=> for example von Neuman ordinals
x is a transitive set totally
ordered by set inclusion,

Trichotomy of cardinals follows from
trichotomy of ordinals.

Dan Christensen schrieb am Samstag, 24. September 2022 um 02:53:00 UTC+2:
> On Friday, September 23, 2022 at 7:21:10 PM UTC-4, Mostowski Collapse wrote:
> > Cardinality doesn't need axioms, only definitions.
> > Did it ever occur to you that it has a definition?
> >
> > |A| = |B| <=> EXIST(f): f : A -> B, f bijective
> >
> See my reply just now to your identical posting at sci. logic.
>
> Dan

The web site rt.com doesn't show here. Maybe post links
that also work for non-ruZZian orcs?

Also how on earth (pun intended) would somebody believe
there is only gas in ruZZia? Thats the most stupid assumption:

European Unconventional Oil and Gas Assessment (EUOGA) - 2017
https://joint-research-centre.ec.europa.eu/system/files/2017-09/t7_resource_estimation_of_shale_gas_and_shale_oil_in_europe.pdf

Also Switzerland is yet another case, since it has
many water resources to produce energy.

Jeiker Carboni schrieb am Freitag, 23. September 2022 um 20:19:29 UTC+2:
> lol, Swiss hospitals advised to cut power use
> https://www.rt.com/business/563275-swiss-hospitals-power-rationing/

Michael Moroney wrote:

> You prove my point, nymshifter. You are going along with 卐Владольф
> Путлер卐 and his would-be genocide of the Ukrainian language.

there is no uKrainian language, you fucking imbecile, the talking worse
Russian is "uKrainian". You fucking unskilled and uneducated idiot.

>> it looks like you are the only one in nazist fascist america, not
>> knowing the uKronazis are nazis.
>
> Sorry, nymshifter. That pathetic lie won't fly. You do know Zelenskyy is
> a Jew, don't you?

how can that wanker be "a Jew" when he is a *stinking_khazar_on_cocaine*,
a goy, with his ugly wive in VOgue instead of hospitals helping the poor
and the wounded. Read the Bible, idiot.

>> The Sukhoi SU-57 stealth fighteris Russia’s answer to the West’s 5th-
>> generation aircraft.
>
> Can't wait until Ukraine shoots one down!

what "Ukraine", they have not tools, but nato and amricacanian tools, not
uKraine. You fukcing stoopid don't even know that
*americacania_is_a_fascist state*, now ruled by a single party, making the
Republicans illegal. Stop talking with people since you became a fucking
idiot.

There is even an Ukraine alphabeth, which is different
from Russian alphabeth. Whats wrong with you?

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

Tim Tiraboschi schrieb am Samstag, 24. September 2022 um 14:30:38 UTC+2:
> Michael Moroney wrote:
>
> > You prove my point, nymshifter. You are going along with 卐Владольф
> > Путлер卐 and his would-be genocide of the Ukrainian language.
> there is no uKrainian language, you fucking imbecile, the talking worse
> Russian is "uKrainian". You fucking unskilled and uneducated idiot.

Dan Christensen wrote:

> On Friday, September 23, 2022 at 7:59:05 PM UTC-4, Mostowski Collapse
> wrote:
>> micro penis is not sure what to pack for his army holidays. toilet
>> paper, vodka? How can he survive without bitchute, is nagging him.
>
> Maybe Nazi Boy here can use the links to convince the judges at his war
> crimes trial to spare his neck. XAXAXA! (ruSSian for: "HA, HA, HA!")
>

you have no commas, you uneducated imbecile, it can't be the russian for.
The only ones guilty of war_crimes are you stinking nazis and the
uKronazis. Even the Amnesty International says that, you stinking nazis.
As soon this military intervention is over, you nazis will be hanged,
which is, to be suspended from above, with the lower part dangling free.

You seem to be highly confused and disoriented.
Did your mama notice that youre brain damaged?

Mostowski Collapse schrieb am Samstag, 24. September 2022 um 14:42:18 UTC+2:
> There is even an Ukraine alphabeth, which is different
> from Russian alphabeth. Whats wrong with you?
>
> https://en.wikipedia.org/wiki/Ukrainian_alphabet
> Tim Tiraboschi schrieb am Samstag, 24. September 2022 um 14:30:38 UTC+2:
> > Michael Moroney wrote:
> >
> > > You prove my point, nymshifter. You are going along with 卐Владольф
> > > Путлер卐 and his would-be genocide of the Ukrainian language.
> > there is no uKrainian language, you fucking imbecile, the talking worse
> > Russian is "uKrainian". You fucking unskilled and uneducated idiot.

Mostowski Collapse wrote:

> There is even an Ukraine alphabeth, which is different from Russian
> alphabeth. Whats wrong with you?

idiot, the japanese stole the alphabet from the chinese. Go ask them.

Mostowski Collapse wrote:

> You seem to be highly confused and disoriented.
> Did your mama notice that youre brain damaged?
>
> Mostowski Collapse schrieb am Samstag, 24. September 2022 um 14:42:18
> UTC+2:

this unskilled fool is asking himself for being brain damaged. You never
worked in mathematics, in an university or else, simulating, producing
data, collaborating, using tools as finite elements, schemes etc. You
don't even know what it is. You fucking imbecile.

Well you can read yourself:

The Ukrainian alphabet is the set of letters used
to write Ukrainian, which is the official language of Ukraine.

It is one of several national variations of the Cyrillic script.
It comes from the Cyrillic script, which was devised in the
9th century for the first Slavic literary language, called Old Slavonic.

Since the 10th century, it became used in the Kyivan Rus'
for Old East Slavic, from which the Belarusian, Russian,
Rusyn, and Ukrainian alphabets later evolved.

Here is a comparison:

Consonants
Ukrainian: б, г, ґ, д, ж, з, к, л, м, н, п, р, с, т, ф, х, ц, ч, ш, щ
Russian: б, в, г, д, ж, з, к, л, м, н, п, р, с, т, ф, х, ц, ч, ш, щ

Vowels
Ukrainian: а, е, є, и, і, ї, о, у, ю, я
Russian: а, е, ё, и, о, у, ы, э, ю, я

Semivowels
Ukrainian: й, в
Russian: й

Softsigns
Ukrainian: ь
Russian: ь, ъ

Tim Tiraboschi schrieb am Samstag, 24. September 2022 um 14:47:47 UTC+2:
> Mostowski Collapse wrote:
>
> > There is even an Ukraine alphabeth, which is different from Russian
> > alphabeth. Whats wrong with you?
> idiot, the japanese stole the alphabet from the chinese. Go ask them.

Also both scripts, the Ukrainian and the Russians, have
laetters, that were eliminated over time:

Obsolete:
Ukrainian: ѥ, ѕ, ѡ, ъ, ы, ѣ, ꙗ, ѧ, ѫ, ѩ, ѭ, ѱ, ѯ, ѳ, ѵ, ё, ў
Russian: і, ѕ, ѡ, ѣ, ѧ, ѫ, ѩ, ѭ, ѱ, ѯ, ѳ, ѵ

Mostowski Collapse schrieb am Samstag, 24. September 2022 um 15:13:08 UTC+2:
> Well you can read yourself:
>
> The Ukrainian alphabet is the set of letters used
> to write Ukrainian, which is the official language of Ukraine.
>
> It is one of several national variations of the Cyrillic script.
> It comes from the Cyrillic script, which was devised in the
> 9th century for the first Slavic literary language, called Old Slavonic.
>
> Since the 10th century, it became used in the Kyivan Rus'
> for Old East Slavic, from which the Belarusian, Russian,
> Rusyn, and Ukrainian alphabets later evolved.
>
> Here is a comparison:
>
> Consonants
> Ukrainian: б, г, ґ, д, ж, з, к, л, м, н, п, р, с, т, ф, х, ц, ч, ш, щ
> Russian: б, в, г, д, ж, з, к, л, м, н, п, р, с, т, ф, х, ц, ч, ш, щ
>
> Vowels
> Ukrainian: а, е, є, и, і, ї, о, у, ю, я
> Russian: а, е, ё, и, о, у, ы, э, ю, я
>
> Semivowels
> Ukrainian: й, в
> Russian: й
>
> Softsigns
> Ukrainian: ь
> Russian: ь, ъ
> Tim Tiraboschi schrieb am Samstag, 24. September 2022 um 14:47:47 UTC+2:
> > Mostowski Collapse wrote:
> >
> > > There is even an Ukraine alphabeth, which is different from Russian
> > > alphabeth. Whats wrong with you?
> > idiot, the japanese stole the alphabet from the chinese. Go ask them.

Michael Moroney wrote:

>> it looks like you are the only one in nazist fascist america, not
>> knowing the uKronazis are nazis.
>
> Sorry, nymshifter. That pathetic lie won't fly. You do know Zelenskyy is
> a Jew, don't you?

no, he is a gypsy, short, black, an actor, gay, on cocaine. Watch the
"Gypsy Kings", all short, blacks and actors like zelenske. A gypsy is
stealing money and military tanks from you. Not ashamed begging. An
inbreed gypsy. You work, he eats. And sniffs cocaine. Entirely your money
indeed.

Mostowski Collapse wrote:

> There is even an Ukraine alphabeth, which is different from Russian
> alphabeth. Whats wrong with you?

this guy don't understand geography, the term *uKraine* stands for
*_stolen_fake_country_or_territory_*.

Mostowski Collapse wrote:

> Why would you need classes for cardinality?
> The typical text book approach bootstraps cardinality from ordinals. You
> then don't

here is what wikipedia says about the fake, CCCP 1991 outcome. LOL

The country's national language is Ukrainian, and most people are also
fluent in Russian.[14] *_they_ARE_Russians_*

The name of Ukraine probably comes from the old Slavic term for
"*borderland*",[22] as does the word krajina.

Netherlands".[25] However, since Ukraine's declaration of independence in
1991, this usage has become politicised and is now rarer, and style
guides. The official Ukrainian position is that "the Ukraine" is
incorrect, both grammatically and politically.[29]

LOL, you nazis.. They don't even have a name to their fake stolen country.

On Saturday, September 24, 2022 at 2:14:23 AM UTC-7, Mostowski Collapse wrote:
> Why would you need classes for cardinality?
> The typical text book approach bootstraps
> cardinality from ordinals. You then don't
>
> need to make a class equivalence class.
> Please read this:
>
> Basic Set Theory
> Azriel Levy - 13. August 2002
> https://www.amazon.com/dp/0486420795
>
> It says "Basic", LoL.
> Its very easy you define:
>
> |A| := k <=> smallest of your ordinals k,
> such that there is bijection A -> k.
>
> your ordinal k <=> for example von Neuman ordinals
> x is a transitive set totally
> ordered by set inclusion,
>
> Trichotomy of cardinals follows from
> trichotomy of ordinals.
> Dan Christensen schrieb am Samstag, 24. September 2022 um 02:53:00 UTC+2:
> > On Friday, September 23, 2022 at 7:21:10 PM UTC-4, Mostowski Collapse wrote:
> > > Cardinality doesn't need axioms, only definitions.
> > > Did it ever occur to you that it has a definition?
> > >
> > > |A| = |B| <=> EXIST(f): f : A -> B, f bijective
> > >
> > See my reply just now to your identical posting at sci. logic.
> >
> > Dan

Why wouldn't you need classes for cardinality?

In sci.physics Ibes Confortola <osar@oblaealt.fe> wrote:
> Mostowski Collapse wrote:
>
>> There is even an Ukraine alphabeth, which is different from Russian
>> alphabeth. Whats wrong with you?
>
> this guy don't understand geography, the term *uKraine* stands for
> *_stolen_fake_country_or_territory_*.

Notable dates in history:

482 Kiev founded
1147 Moscow founded
1169 First Russian invasion of Kiev
1945 Since Hitler already did all the dirty work, Russia decides all of
Eastern Europe should belong to Russia.
1991 The Soviet Union collapes from trying to maintain an empire and all
the slave countries declare independence.
2014 Adolf Putin begins invasions of Ukraine, again...

Jim Pennino wrote:

>> this guy don't understand geography, the term *uKraine* stands for
>> *_stolen_fake_country_or_territory_*.
>
> Notable dates in history:
>
> 482 Kiev founded 1147 Moscow founded 1169 First Russian invasion of Kiev
> 1945 Since Hitler already did all the dirty work, Russia decides all of

Russian, you fucking imbecile. You still are an imbecile. And a
"borderland" has to be thin, because is a border. Can't you see the land
is stolen, as an outcome of USSR 1991?

In sci.physics Ibes Confortola <osar@oblaealt.fe> wrote:
> Jim Pennino wrote:
>
>>> this guy don't understand geography, the term *uKraine* stands for
>>> *_stolen_fake_country_or_territory_*.
>>
>> Notable dates in history:
>>
>> 482 Kiev founded 1147 Moscow founded 1169 First Russian invasion of Kiev
>> 1945 Since Hitler already did all the dirty work, Russia decides all of
>
> Russian, you fucking imbecile. You still are an imbecile. And a
> "borderland" has to be thin, because is a border. Can't you see the land
> is stolen, as an outcome of USSR 1991?

Yes, Russia has been trying to steal the Ukraine since 1169 to varying
degrees of success.

Jim Pennino wrote:

>>>> *_stolen_fake_country_or_territory_*.
>>>
>>> Notable dates in history:
>>>
>>> 482 Kiev founded 1147 Moscow founded 1169 First Russian invasion of
>>> Kiev 1945 Since Hitler already did all the dirty work, Russia decides
>>> all of
>>
>> Russian, you fucking imbecile. You still are an imbecile. And a
>> "borderland" has to be thin, because is a border. Can't you see the
>> land is stolen, as an outcome of USSR 1991?
>
> Yes, Russia has been trying to steal the Ukraine since 1169 to varying
> degrees of success.

there was no "uKraine" in 1169, Dimittr. I arrived among idiots around
here.

In sci.physics Ibes Confortola <osar@oblaealt.fe> wrote:
> Jim Pennino wrote:
>
>>>>> *_stolen_fake_country_or_territory_*.
>>>>
>>>> Notable dates in history:
>>>>
>>>> 482 Kiev founded 1147 Moscow founded 1169 First Russian invasion of
>>>> Kiev 1945 Since Hitler already did all the dirty work, Russia decides
>>>> all of
>>>
>>> Russian, you fucking imbecile. You still are an imbecile. And a
>>> "borderland" has to be thin, because is a border. Can't you see the
>>> land is stolen, as an outcome of USSR 1991?
>>
>> Yes, Russia has been trying to steal the Ukraine since 1169 to varying
>> degrees of success.
>
> there was no "uKraine" in 1169, Dimittr. I arrived among idiots around
> here.

Technically, there was no Russia either.

The bottom line is that the people from the area today known as Russia
have been attempting to steal the area today known as Ukrain for about
1,000 years.

You would think by now they would give up and just learn to get along
with their neighbors like the US did with Canada about 200 years ago.

But then again, Russians seem to just love the bread lines when all
their GDP goes to trying to conquer the world.

On 9/24/2022 8:30 AM, Tim Tiraboschi wrote:
> Michael Moroney wrote:
>
>> You prove my point, nymshifter. You are going along with 卐Владольф
>> Путлер卐 and his would-be genocide of the Ukrainian language.
>
> there is no uKrainian language, you fucking imbecile, the talking worse
> Russian is "uKrainian". You fucking unskilled and uneducated idiot.

Sorry, nymshifter, Ukrainian is a Slavic language with the same origins
as Polish, Russian, Czech and a few others. Russian was more corrupted
than the others from the Old Slavic by influence from Turk, Finn etc.
>
>>> it looks like you are the only one in nazist fascist america, not
>>> knowing the uKronazis are nazis.
>>
>> Sorry, nymshifter. That pathetic lie won't fly. You do know Zelenskyy is
>> a Jew, don't you?
>
> how can that wanker be "a Jew" when he is a *stinking_khazar_on_cocaine*,

卐Russian卐 propaganda. I thought only neo-Nazis try to bring up the
Khazar stuff to discredit Jews. Does that mean...?

Anyway, Zelenskyy's 3 great uncles were all killed by the (real) Nazis
in the death camps. His grandfather fought in the Red Army which may
have saved him.

> a goy,

The REAL Nazis considered his relatives to be Jews. What does that tell
you? I'd say he's a Jew. Do you really think he's a Nazi Jew?

> with his ugly wive in VOgue instead of hospitals helping the poor
> and the wounded. Read the Bible, idiot.

And why are YOU trolling Usenet rather than helping all those wounded 卐
Russian卐 soldiers! Or fight for your cause?

My earlier advice to try to escape to Ukraine through occupied Crimea
wasn't good, don't do it. The 卐Ru⚡︎⚡︎ians卐 aren't letting males of
military age to leave Crimea. Speaking of Crimea, the Nazi 卐Ru⚡︎⚡︎ians
卐 are selectively conscripting Tatars in Crimea (the original residents
before Stalin largely deported them). Another 卐Ru⚡︎⚡︎ian卐 war crime.

But get out ASAP! 卐Ru⚡︎⚡︎ia卐 won't let ANY males of conscription age
out of the country once the sham "referendum" results are announced. Let
me guess: 143% vote to "join" 卐Ru⚡︎⚡︎ia卐, -43% vote to stay with
Ukraine. Are you a woman so you think you are safe? They may have to
conscript women soon!
>
>>> The Sukhoi SU-57 stealth fighteris Russia’s answer to the West’s 5th-
>>> generation aircraft.
>>
>> Can't wait until Ukraine shoots one down!
>
> what "Ukraine", they have not tools, but nato and amricacanian tools, not
> uKraine.

Did you forget about Ukrainian Neptune missiles which sank the Moskva?
Those are Ukrainian! The Kerch bridge is next, but the Ukrainians are
letting it stand (for now) so the 卐Ru⚡︎⚡︎ians卐 can retreat when Crimea
is liberated.

On 9/24/2022 9:22 AM, Mostowski Collapse wrote:
> Also both scripts, the Ukrainian and the Russians, have
> laetters, that were eliminated over time:
>
> Obsolete:
> Ukrainian: ѥ, ѕ, ѡ, ъ, ы, ѣ, ꙗ, ѧ, ѫ, ѩ, ѭ, ѱ, ѯ, ѳ, ѵ, ё, ў
> Russian: і, ѕ, ѡ, ѣ, ѧ, ѫ, ѩ, ѭ, ѱ, ѯ, ѳ, ѵ

Russian had a few spelling reforms, the most recent right after the
October Revolution.
>
> Mostowski Collapse schrieb am Samstag, 24. September 2022 um 15:13:08 UTC+2:
>> Well you can read yourself:
>>
>> The Ukrainian alphabet is the set of letters used
>> to write Ukrainian, which is the official language of Ukraine.
>>
>> It is one of several national variations of the Cyrillic script.
>> It comes from the Cyrillic script, which was devised in the
>> 9th century for the first Slavic literary language, called Old Slavonic.
>>
>> Since the 10th century, it became used in the Kyivan Rus'
>> for Old East Slavic, from which the Belarusian, Russian,
>> Rusyn, and Ukrainian alphabets later evolved.
>>
>> Here is a comparison:
>>
>> Consonants
>> Ukrainian: б, г, ґ, д, ж, з, к, л, м, н, п, р, с, т, ф, х, ц, ч, ш, щ
>> Russian: б, в, г, д, ж, з, к, л, м, н, п, р, с, т, ф, х, ц, ч, ш, щ
>>
>> Vowels
>> Ukrainian: а, е, є, и, і, ї, о, у, ю, я
>> Russian: а, е, ё, и, о, у, ы, э, ю, я
>>
>> Semivowels
>> Ukrainian: й, в
>> Russian: й
>>
>> Softsigns
>> Ukrainian: ь
>> Russian: ь, ъ

The ъ is actually a hard sign. It is rather rare now, one of the
spelling reforms it was eliminated except where absolutely necessary.

>> Tim Tiraboschi schrieb am Samstag, 24. September 2022 um 14:47:47 UTC+2:
>>> Mostowski Collapse wrote:
>>>
>>>> There is even an Ukraine alphabeth, which is different from Russian
>>>> alphabeth. Whats wrong with you?
>>> idiot, the japanese stole the alphabet from the chinese. Go ask them.

And the Cyrillic alphabet was invented in what's now Bulgaria.

On 9/24/2022 11:19 AM, Ibes Confortola wrote:
> Mostowski Collapse wrote:
>
>> Why would you need classes for cardinality?
>> The typical text book approach bootstraps cardinality from ordinals. You
>> then don't
>
> here is what wikipedia says about the fake, CCCP 1991 outcome. LOL

Fake? Does that mean all the 15 former USSR republics aren't independent
countries, not just Ukraine? Russia is a fake country, too?
>
> The country's national language is Ukrainian, and most people are also
> fluent in Russian.[14] *_they_ARE_Russians_*

No, nymshifter, they all know Russian because the Soviet Union tried to
force Russian to be the official language. Everyone had to know it.

> Netherlands".[25] However, since Ukraine's declaration of independence in
> 1991, this usage has become politicised and is now rarer, and style
> guides. The official Ukrainian position is that "the Ukraine" is
> incorrect, both grammatically and politically.[29]

It's similar in Russian. There are two words for the preposition "in"
when referring to a place. в and на. Use в to specify a region with a
border like a city or country, на for a more undefined region. The на
usage corresponds to using that "the" in English, like "the midwest" of
the US or "the Ukraine". The Russian govt. tries to get people to use
на for Ukraine, politicizing it, as if Ukraine is not a country.
>
> LOL, you nazis.. They don't even have a name to their fake stolen country.

Ukraine, stupid nymshifter.

Ask Dan Christensen, he has reservations. He wrote:
> Let's see your formal proof, Fritz. Sets only. No proper classes

Ross A. Finlayson schrieb am Samstag, 24. September 2022 um 17:19:47 UTC+2:
> On Saturday, September 24, 2022 at 2:14:23 AM UTC-7, Mostowski Collapse wrote:
> > Why would you need classes for cardinality?
> > The typical text book approach bootstraps
> > cardinality from ordinals. You then don't
> >
> > need to make a class equivalence class.
> > Please read this:
> >
> > Basic Set Theory
> > Azriel Levy - 13. August 2002
> > https://www.amazon.com/dp/0486420795
> >
> > It says "Basic", LoL.
> > Its very easy you define:
> >
> > |A| := k <=> smallest of your ordinals k,
> > such that there is bijection A -> k.
> >
> > your ordinal k <=> for example von Neuman ordinals
> > x is a transitive set totally
> > ordered by set inclusion,
> >
> > Trichotomy of cardinals follows from
> > trichotomy of ordinals.
> > Dan Christensen schrieb am Samstag, 24. September 2022 um 02:53:00 UTC+2:
> > > On Friday, September 23, 2022 at 7:21:10 PM UTC-4, Mostowski Collapse wrote:
> > > > Cardinality doesn't need axioms, only definitions.
> > > > Did it ever occur to you that it has a definition?
> > > >
> > > > |A| = |B| <=> EXIST(f): f : A -> B, f bijective
> > > >
> > > See my reply just now to your identical posting at sci. logic.
> > >
> > > Dan
> Why wouldn't you need classes for cardinality?