I never said they were similar. I said one shouldn't harbor illusions about Ukraine being a sovereign, independent state if it enters the EU or NATO, like none of the member states of those institutions are. — Tzeentch

Then obviously you have an incorrect idea of what is to be a sovereign state. There's an interconnected web of international laws, agreements and international cooperation that limits the sovereignty of the individual state. That simply is the reality in the modern World. And as clearly seen with Brexit, EU has it's advantages just why so many countries have chosen to stick together.

That countries have voluntarily chosen to join these institutions makes it different. It makes all the difference in the World compared to a military invasion an sham referendums.

he US controls NATO. NATO countries are vassals of the US, because they rely completely on the US to keep them safe.

The EU demands an even greater sacrifice of autonomy, because it also gets legislative power inside EU countries. It's purpose is/was to become a "United States of Europe", essentially, of course still completely dependent on the United States for protection.

So lets not harbor illusions about countries in NATO or the EU being sovereign. — Tzeentch

You can utilize what kind of discourse of vassalization whatever about the EU or being in NATO, but it totally falls to be similar with the case of an autocratic dictatorship where speaking of a war as a war can get one long prison sentences... and a country which has either gone to war or created frozen conflicts with three of it's neighbors.

Just to give an example, the vast majority of the people in this country wanted to join NATO and the Parliament heard their calls and voted to join NATO (with far larger majority than EU) as everybody understood that neutrality was meaningless for Russia's ambitions. Countries have joined voluntary both NATO and EU. And the reason seems to be confusing for some here.

The case where the US has imposed it's force, the result has been utter failure (Afghanistan) and extremely bad and tense relations (Iraq). Somehow you don't get friends by bombing the people first.

But don't let such facts hinder your logic of the West being "vassals of the US" and the straightforward comparison then to the empire building with war, violence and annexations as Putin's Russia is doing.

The choice has been between Russia or the United States to control Ukraine. — Tzeentch

Think for a while about it.

Is the US annexing parts of Ukraine?
Does the US think Ukraine is an artificial state and should belong to American culture and English be spoken and taught in schools?
Does the US want to demolish Ukraine?
Is the US forcing people to transfer to the US?

And Ukraine would want to join the EU. Wouldn't the EU then "control" Ukraine far more than the US?

The idea of the US being in control in similar fashion than Putin is simply absurd. Ukraine is really fighting for it's existence to be a sovereign state.

A cardinal number is, well, a number. When we talk about finite sets, the cardinal number is a natural number.

And even if this will irritate the mathematicians here, we do use infinity quite a lot, we just don't talk about it as infinity. Just like with limit sequences and limit points etc.

Why ought Ukraine have control over Crimea/Donbas? There's no god-given right to any piece of land, there's no racial-biological link to Ukraine, there's no harm-reduction principle... There's no grounds at all been offered as to why they ought have that land. — Isaac

Why ought Russia have the right to take it from a sovereign state, whose territories it has accepted on several occasions? Why ought violence, aggression and straightforward imperialism justified?

But for you it doesn't matter if Putin is control of Ukraine or the Ukrainians are in control of Ukraine, hence this conversation has utterly no meaning. You just reinforce the stereotype of a typical tankie, for whom US and the West is evil and nothing else matters.

Why not just use a normal investment rather than the cryptocurrency scam? Apparently the standard index funds have an annual return of around 10%. — Michael

Index funds may really not be the great investment now, just as @Benkei noted.

What I think is obvious that they mobilized are used in the classic Russian way as cannon fodder. I remember some Ukrainian soldiers that were interviewed said that the new mobilized troops were used in a way he never imagined troops would be used. Hence there is absolutely far too many incidents reported that this would be propaganda.

The simple fact is that the Russian Army was totally incapable of handling hundreds of thousands of mobilized troops at once. Annually in peace time Russia takes in a quarter of million of conscripts, 100 000+ in two batches. They are then basically trained in the units...that now are deployed in Ukraine. So where do you have the spare people to train suddenly 300 000? Nowhere. It basically will take them years to create an organization to train such huge masses. This is the simple reason why it's such a mess.

Even my country, Finland, would have severe problems after it mobilized the 280 000 war time force. Yes, the country has potentially 700 000 reservists. But once the 280 000 are deployed, there is nobody to train the next batch of conscripts than reservists themselves: all the professional officers are acting as commanders in the fielded army. As the army is fully oriented to being a reservist army and focus on that mission, it could be overcome, but then take Russia, an army that has tried to do away with conscription and didn't have an organization to mobilize hundreds of thousands. This is the simple unavoidable end result.

That those are then shot by the their own troops I would be skeptical, too crazy. Stalin's army with straf battalions? What is obvious that without anything else and without the ability to train the troops, they are used in this way. Perhaps the idea is to go through the winter and have then the next batch of conscripts ready and trained for the spring. After all, now as these parts of Ukraine are part of Russia, you can use the conscripts there.

But that won't change the endemic corruption among the armed forces and the utter lack to train such large forces. Just an example of the theft:

A recent investigation by BBC News Russian showed that, over the last eight years, military courts have issued more than 550 sentences for theft of clothing from army stocks. In total, during the same period, court data revealed that more than 12,000 corruption cases were opened involving the theft of military gear and equipment, with some cases occurring even after Russia invaded Ukraine.

And why is the West's policy to not go into Ukraine, no no-fly-zone, as well as severely limit weapons systems to Ukraine?

Resulting in this situation where Russia has no particular need to use nuclear weapons. — boethius

That is where nuclear weapons work: deterrence. If this would be a non-nuclear armed country attacking Ukraine, it is likely that a no-fly zone would have been enforced.

And it works both ways: Russia doesn't dare to attack the countries supplying arms to Ukraine or training Ukrainian troops.

China may have zero problem with Russia nuking NATO troops in Ukraine — boethius

Wrong.

“The international community should … jointly oppose the use or threats to use nuclear weapons, advocate that nuclear weapons must not be used and nuclear wars must not be fought, in order to prevent a nuclear crisis in Eurasia,” Xi said.

China has warned Russia against threatening to use nuclear weapons in the conflict in Ukraine, in a rare departure from its usual tacit support for Moscow’s positions.

The warning came during talks on Friday between Chinese leader Xi Jinping and German Chancellor Olaf Scholz in Beijing, according to Mr. Scholz and the Chinese state news agency Xinhua.

Messrs. Xi and Scholz agreed to oppose the use or threat of use of nuclear weapons, according to Mr. Scholz and a report by Xinhua, which normally echoes Beijing’s official positions.

Trade relations with the West are important to China, you know.

... Like Belarus and Kazakstan and Georgia? — boethius

Two of the need a lot of work. Even if Russia did help the regime survive in Kazakhstan, they didn't turn the favour for Putin. Haven't gone along with the annexations and have given refuge to those fleeing the mobilization.

What is the next step of this "rebuild the Soviet Union" plan? — boethius

Not the Soviet Union, just Russia. With Putin you have the closest to a Russian Czar, actually. Only that he doesn't have a son waiting in the sidelines to become the next President.

As some have:

What Putin did next was negotiate Mink I — boethius

Minsk I (not Mink I) came only after Ukraine had fought the insurgents to a standstill (and the Russian army did have to save their asses a few times).

which Ukraine didn't respect — boethius

Which both sides didn't respect.

However, the more important question remains what we can do about it. — boethius

After Russia first declared the puppet regimes independent (in a choreographed meeting which an intelligence chief fumbled and got mixed with the next chapter, annexation) and then annexed not only them, but also more areas of Ukraine (parts of it which Russian forces don't even occupy), the Minsk procedures have been long dead and buried. Conveniently you are forgetting all the annexations that Russia has done.

Let's say Ukrainians form a bridge head over an important river and need to pour in significant resources to consolidate that bridge head ... drop a nuke on said bridge head and not only all those forces are gone, but it become clear that there is basically no way to ford the river in peace.

The idea Nuclear weapons have no military use is just insanely naive. — boethius

Why wouldn't you use a smart bomb, enough conventional missiles or artillery to destroy the bridge? Absolutely no threat of NATO getting involved. Good if the media even would pick it up, but it wouldn't cause any outrage. This is where the stupidity lies in using nuclear weapons. If you really think that it's "naive" not to use nuclear weapons, then just why aren't people using them?

Or you have now become and adherent for tactical nuclear weapons?

It seems, if what you say is true, Russia can suffer some acceptable losses for the privilege of nuking Ukraine.

There would be a "cost of doing business" is what you are saying? — boethius

There are escalatory ladders. But basically yes, there is a "cost of doing business" with nuclear weapons. Russia cannot dismiss the West's response of a conventional attack as a bluff. Of course, it could be a bluff, but I don't think they want to find out.

Again, maybe just explains why the US and NATO aren't actually escalating to "help Ukraine win" which is why Ukraine has so far not won and suffering immensely for the honour of representing Western interests, in some vague way. — boethius

As I said, there are two reasons why Ukraine isn't getting everything it wants:

1) Yes, there can be those who think of it as escalation and worry that for example longer range artillery rockets would be used to attack targets inside Russia proper (which actually Ukraine has done by it's own weapon systems).

2) The arm cache of the West isn't actually so big and new weapons cost much. The world economy is going to a recession and spending on military in Ukraine is costly and doesn't create jobs much if any, actually. The West's arms procurement is made for peace time, not for a long conventional war.

The key question of the recent dialogue is "at what cost to Ukraine?" and is this cost reasonable to ask a proxy to pay.

You and all the other Zelenskyites simply keep dodging the question. — boethius

Oh yes, the Ukrainians as the "proxies" of the evil West. How typical, the victim is the proxy.

Simply keep the same level as now. Keep the course now set. Let's see after next year. As long as Ukrainians are willing to fight, it's their decision. It is them who are actually paying the cost, not us. If they aren't willing to fight, then military aid is useless.

This is the central absurdity of the West's position. It argues right up to its policy line with extreme rhetoric, standing up to Putin, Churchillian "never surrender" type stuff, Putin's a war criminal and the Russians are literally terrorists, and the entire world order is at risk, and basically the greatest moral imperatives you can think of etc. But when it comes to the question of "well, why not do more then, send modern tanks and fighter jets or then go in with our own planes and troops" the exact opposite direction of appeasement is argued that "of course the nukes". Well ... which one is it? Are we "doing what it takes" and fighting on the fields and beaches and and in the air and seas and so on, or are we actually tiptoeing around any actual risk to the Kremlins core goals and making clear we are appeasing with respect to those core goals so no need for any desperate measures? — boethius

Notice the difference with rhetoric and actions on the Russian side too. Russians have basically made the argument that they already are fighting NATO... when they are fighting Ukrainians armed with Western weapons and support.

And notice one limitation here: NATO does also have to upkeep it's own forces. Only the Baltic states have basically given all-out support plus the kitchen sink. Javelins are a good example: a huge portion of all Javelins have been sent to Ukraine means that the US to produce the systems to replace these will take two years I remember.

We have to remember that the armed forces of West European countries are small compared to Ukraine (and Russia). Ukraines army is now estimated to be 500 000 to 750 000. That is a huge army to arm, when by European standards the mobilized Finnish army is huge (less than 300 000).

This is what shouldn't be forgotten: The Ukraine war is a conventional war and because it wasn't a short two week war, it's draining the hell out of everybody. Yes, Russia has had to rely on antiquated tanks and ancient Cold War weapon systems because it doesn't have anything else. Well, don't think the West this would be different. The weapons manufacturing in the West is designed for small wars, small limited operations and procurement of small batches of expensive weapon systems. Not to feed a WW1/WW2 style weapons manufacturing juggernaut needed to provide sufficient materiel to the mouth of Moloch.

Encourage Putin to do what exactly? — boethius

Simple: to continue to undo "the greatest tragedy of the 2oth Century". Russia to claim dominance over it's "near abroad".

And the West has given him this: After annexing Crimea and starting in limited insurgency in the Donbas, what did Putin do? He took take the next step to make a large scale attack on Ukraine. Did then the West and NATO respond as it has now? No, not back in 2014. There's your example from history.

You really think he would be satisfied with Novorossiya and a puppet regime in Kyiv? No. Then there's Moldova. It's so clear and obvious when you read actually what Putin has said. And done.

Radiation isn't all that big a concern when it comes to tactical nuclear weapons. — boethius

Tell that to people. (I have to remember to quote you later.) And btw radiation on the site where a tactical nuke has been used, it is a problem.

The utility of nuclear weapons would be in the scenario where Ukraine is actually advancing a sizeable concentration of force. Dispersed forces are a defensive measure and not an offensive measure. — boethius

Again you have no idea what you are talking about. In the age of drones and instant fire-missions that can rain down in few minutes, artillery poses a threat at any time to any concentration of force. That's why you don't see columns of Ukrainian tanks... or nowdays of Russian armour moving along in long columns also. The unit size is smaller than before (Soviet doctrine was to operate with fronts and armies). This is obvious from the fact that the Russian forces, already before the war started, were deployed as Battalion-combat-teams. You don't operate with larger formation, brigades, divisions as in WW2 or as during the Cold War.

Definitely. However, the question is what escalation the West would do that would be responded to with Nuclear weapons by Russia ... that the West would then not respond with nuclear weapons. — boethius

I think it's obvious from what has been leaked even to the public. A conventional attack on Russian forces in Ukraine and Naval ships operating in the Black Sea. Hence notice the level of escalation: Russian sites in Russia aren't attacked. Then again Russia has an option to escalate: does it enlarge the battlefield to outside Ukraine and the Black Sea.

Let's remember that for example in the Korean war the Soviet Air Force fought the USAF on a limited airspace next to the Chinese border. That indeed the two Superpowers were engaged in fighting was simply kept a secret by both sides not wishing to escalate matters.

But then again, this is the "sabre rattling" to Russia's "sabre rattling" in the first place. What actually NATO would do or not is another thing. Medvedev could be right and NATO wouldn't do anything, but be outraged.

Appeasing the bully will just encourage Putin. The nuclear sabre rattling naturally is taken seriously, but it should be looked just how likely this would be.

- China is against the use of nuclear weapons in Ukraine.
- There's a serious risk of this escalating the war and not cowing the West push for cessation of fighting, but to do the opposite.
- Ukraine is next to Russia, hence radiation can easily travel to Russia by winds.
- Destroying Ukrainian forces with tactical nuclear weapons is difficult: troops on the modern battleground are very dispersed.
- Ukraine is unlikely to surrender or to give in just by using tactical nuclear weapons.
- Forces operating in nuclear fallout areas will need training and equipment Russia doesn't have now: basically you will create a small no-go zone for your troops also.
- After the initial quick-capture strategy went bust (on day one) and created the logistical fiasco, Russia has actually been very risk-averse. The withdrawal from Kherson (and Kyiv) shows this. Suddenly such an escalation would go against the way that Russia has fought the war after the initial push.
- Russia has no interest to initiate World War 3. If the "Escalate to De-escalate" doesn't work, then there is nothing to gain from this kind of escalation. It has suffered severe losses in Ukraine already and the last thing would be to escalate the war to a totally new level.

Furthermore, I was even before this war started very worried about the Russian doctrine to "Escalate to De-escalate", meaning that Russia would use at a time of it's convenience and by using the nuclear weapon to create an environment where there is a overwhelming public desire to stop the fighting at all costs immediately.

Yet this isn't 2014 and Russia has no strategic surprise. It had in 2014 the surprise then as just taking off the flag from their combat fatigues and Putin insisting that the VDV paratroops were not Russian soldiers confused the West and especially it's media totally. The "Escalate to de-escalate" strategy would need the West to be already confused about the war, the Western politicians not having had any thought of a nuclear escalation. Then knee-jerk response "STOP EVERYTHING!"

Now as the nuclear sabre-rattling is many months old, Western generals and Western leaders have had ample time to think about their response which makes it likely that NATO can hold it's line together even if Russia did escalate this way. The shuttle diplomacy behind the scenes of intelligence directors sending the message to Russia has made this pretty clear to the Russian leadership. Don't forget that NATO has it's own nuclear deterrence.

And the basic simple fact is that Russia can lose this war. In fact, because there is no opposition and Putin is firmly in control of the country (at least now), he could be just fine even after a disastrous humiliating defeat. Just like Saddam Hussein after the Iran-Iraq war and Desert Storm. Hence the idea that Putin cannot be humiliated is just pandering the dictator.

Showing a well ordering of the set of rational numbers is not adequate for showing that the set of rational numbers is countable. — TonesInDeepFreeze

Countable, right. Thanks for the correction.

To the layman (as me) this is rather scholastic, but I understand that math is precise. So a question:

When you construct "a denumerable binary sequence not in the range of f", aren't you deriving that contradiction? There's the negative reference to f.

After all, when let's say one asks if the set of natural numbers and rational numbers have the same cardinality, there is a direct proof (the set of rational numbers can be well ordered and Cantor showed this).

What was then his working hypothesis?

The argument being made is that Russia getting its way would be bad, but Russia not getting its way would be bad too (nuclear escalation). Therefore some negotiated compromise between the two positions is the best course of action. — Isaac

This is simply irrational.

Neither side will overcome and defeat totally the other side. Hence there will be a negotiated peace or armstice (like between the Koreas). That's the totally logical.

The illogical or delusional reasoning is that "Russia not getting its way would be bad too (nuclear escalation)". Well, many even nuclear armed powers haven't gotten their way in wars. Their defeats have been smaller or larger, but having nukes hasn't change it. Last example was that the US had to withdraw from Afghanistan.

The continuum hypothesis is that the cardinality of the set of reals is aleph_1. That is equivalent to saying that there is no uncountable subset of the set of reals that is not 1-1 with the set of reals. Of course, no matter the continuum hypothesis, there are cardinals greater than aleph_1. — TonesInDeepFreeze

Cantor proved that you cannot make a bijection between the natural number to the reals, hence the reals aren't aleph_0 like for example rational numbers.

The diagonal argument given by Cantor was not a reductio ad absurdum. — TonesInDeepFreeze

When you first assume that there is a bijection between the natural numbers and reals, then show that there is a real that cannot be in this bijection, that is a reductio ad absurdum.

Maybe Monty Python took residence at Zhitnaya Street 14. — jorndoe

Actually, what Russia would need would be it's own Monty Python.

Monty Python, and it's success shows a crucial great aspect of the English, if not the British: the ability to laugh at and ridicule themselves. Naturally an autocratic regime wouldn't tolerate any of it and would see Monty Python as a symptom of the decadence and impotence that the UK fell into after losing the Empire.

Just as an example, think what the reaction would have been during the times of the British Empire, early 20th Century or late 19th Century of the following Monty Python skit, the Queen Victoria Handicap:

https://www.dailymotion.com/video/x32sd40

Nobody would dare to mock Queen Victoria in such way those times. Empires cannot laugh at themselves. Now it is very funny.

And actually this would come easily from the Russians as they have had totalitarian systems that they have joked about. A traumatic history is one of the best ways people find a fountain from jokes and comedy (just think about Jewish humour).

Yet when in the 21st Century a country has laws where uttering the obvious, that the country is in war when it is in a war, can get you jail time, for me it tells that the situation isn't on solid foundations at all. Such urge to limit simple talk is a sign of weakness and fear. And something that is unsustainable without a North Korean type dictatorship.

For the UK the humbling happened during the Suez Crisis and the Churchillian wing in the British leadership understood the the time of Empire acting by it's own was over...and wouldn't be coming back. Yet Monty Python is something that the British have they can be proud of. It shows that the British have no appetite for reconquering their Empire. A politician calling for the unification of the British Isles under the Union Jack, hence occupation and annexation of Ireland, would simply be called what he is: a lunatic. With the British (and they still are the British) we can know that they are quite independently thinking (Brexit and stuff), but they aren't a threat to the sovereignty of Ireland. And furthermore, Scotland, Wales and Northern Ireland are still part of the UK. Something that Russia should understand to do as how to keep it's minorities happy and chugging along.

For Russia to become a normal country and shed it's bellicose aggressive behaviour a humiliating defeat could do it. The Soviet Union came so splendidly and peacefully apart that people like Vladimir Putin understood it as a mistake, something you can and have to fix.

The Putinist empire builders have to become the butt of jokes. Otherwise Russia will pose a threat to it's neighbors. And actually to itself.

I think we are simply talking differently about the subject. But as I'm no mathematician, I acknowledge that my wording might not be rigorous.

Do notice that Cantors system is the sequence of cardinal numbers: aleph_0. aleph_1, aleph_2, aleph_3 and so on. The question is if this hierarchial system holds and if there is a cardinality or not between the naturals or the reals. The continuum hypothesis is that the reals is the next aleph, that there isn't anything else.

Cantor's proof was not by reductio ad absurdum — TonesInDeepFreeze

Your somewhat correct. The first proof in 1874 wasn't. But he did give this in 1891 with the diagonal argument, which I find more simple.

Ukraine does not have allies. Ukraine has arms suppliers.

There's a big difference. Allies would be in Ukraine right now fighting on behalf of their ally. — boethius

Hm.

Comes to mind what a great ally Russia was to Armenia, when it was attacked by the Azeris. Didn't even provide arms, but least after Armenia lost the war held peace talks.

But then for Russia alliances are a way to control and dominate smaller states (hence the Russo-Chinese axis has it's problems).

aleph_1 is the next aleph after aleph_0

is not the continuum hypothesis. — TonesInDeepFreeze

The cardinality of the set of real numbers is aleph_1

is the continuum hypothesis. — TonesInDeepFreeze

As to the other poster, the current question of the continuum hypothesis does not stem from the definition of 'countable'. — TonesInDeepFreeze

Well, it's about what can be put into one-to-one correspondence with the set of natural numbers and the reductio ad absurdum proof that this cannot be done with the set of reals. Here 'countable' has it's problems, when ordinarily everything that we can map into one-to-one correspondence is countable (a+b=c).

When ZF was meant to do away with the paradoxes, it's obvious that it has problems with infinity. After all, it's just taken as an useful axiom.

Putin's only alliance could crumble after special summit shows Russian despot isolated
— Alessandra Scotto di Santolo · Express · Nov 24, 2022 — jorndoe

I wouldn't be surprised. Russia did nothing to help it's ally Armenia when it was attacked. But naturally for Russia alliances don't mean the same thing as for the West. Just like the Warsaw Pact, they are a tool to control the internal situation of the other member countries. And when Russia doesn't have the similar control of CSTO members as it had of it's Warsaw Pact members, then it can only withdraw that help when the country needs it.

And this is noticed in the Central Asian realm as there is the possibility that the consequence of this war can be a lot more than just a humiliating defeat against the Ukrainians.

Your experts do not need to be the same as mine. — Olivier5

Even if they would be the same, Isaac would interpret them totally differently. As he has done.

But that's about infinity, actually. The Continuum Hypothesis.

That's a good return. And you are correct that making an investment where you don't physically meet someone or know where to physically go if there's a problem and it's open for hackers (as I'm lousy in cybersecurity), I wouldn't invest a huge portion of my wealth in. I know, I'm old school.

So seems you are in the microfinancing (or is it people-to-people financing). The Benkei Bank. :smile:

BEIJING, Nov 15 (Reuters) - Chinese President Xi Jinping, discussing Ukraine with U.S. President Joe Biden during their meeting on Monday in Indonesia, said nuclear weapons cannot be used and nuclear wars cannot be fought, according to a statement by the Chinese foreign minister.

This seems to have had an effect on the discussion about using nuclear weapons in Ukraine. Likely the costs of any "Escalation to de-escalation" would be far too big.

The countries that have acknowledged the annexation of Crimea don't include China btw. (They are The countries are: Belarus, Bolivia, Cuba, Afghanistan, Nicaragua, North Korea, Sudan, Syria, Venezuela)

China has simply abstained from both recognizing and discouraging the recognition in the votes in the UN.

Do they have a moral right to some piece of geography? — Isaac

As an Englishman, do you have a moral right to some piece of geography, like where you live?

I can clearly see a moral allowance for fighting back. If someone comes to take what's your by force, it seems fair use equal force to retain it. But I can't see how you're getting from a moral allowance to a moral duty - that they actually ought to fight back, not merely that they could. — Isaac

It's not about duty. It's simply a very rational response. When you can defend and protect yourself from a hostile attack, do so. Russians aren't control of Kyiv as they wanted. They failed to capture it and put a puppet regime in place... and get that Novorossiya, that they have dreamed about.

It's the simple fact that the attack is about imperialism in it's most aggressive, most ugliest form: when your country is "artificial" and actually said to be part of your neighbor, now somehow governed by "neonazis", everybody should understand how bleak the future is under such control. We have already seen the Russification efforts in schools in the occupied territories and the forces evictions/relocations of Ukrainian people and children to Russia. We've seen the mass killings. And the attacks on hospitals and civilians. And you can just follow what actually Russians and above all, what Putin is saying. But you don't, so you think there would be nothing different in Ukraine if it's part of Russia or an independent country.

Why would you as a tankist care because it's not the evil US doing the bad things.

- an unsettled question. — TonesInDeepFreeze

What did I say? There's still something for us to understand with infinity.

Actually, I think the continuum hypothesis is that from aleph_0 the next is aleph_1.

Question: What's the Nmax for our universe? — Agent Smith

Very easy: aleph-1. The the infinite cardinal of the real numbers

Because I think there's still something for us to understand with infinity, it isn't so easy that to use finite logic. And more interestingly, bigger infinities seem not to be usefull for example in physics, computing, etc.

It's a simple question. Ought the Ukrainians fight this imperial aggressor to regain their lost territory? Not "will they?", "ought they?" — Isaac

They naturally ought to fight, and that fight has been proven very successful. An invader that thinks your sovereign state is artificial, that ought to be part of Russia (because of history) and you ought to be Russian and you don't deserve to have your own country, as we have seen from what kind of actions implemented on the occupied territory, is the worst kind of occupier.

But you don't care a damn about the Ukrainians, aren't interested at all and simply have no idea just why they should defend themselves.

When you don't get this kind of truths into your head, as noted, there's no point of continuing this topic with you.

Clueless as ever.

Is the chance of Ukraine regaining their lost territories worth the cost? It's a simple question. How many lives is that region's choice of governance worth? — Isaac

When you in your ignorance (or living in your alternative reality) think there is no difference between Ukraine and Russia...

Ukraine and Russia, however, have quite similar governments, particularly in the East where Ukraine were fighting the pro-Russian breakaway factions. Similar in levels of corruption, similar in human rights, similar in press freedoms, similar in approach to ethnic and national minorities within their territory. — Isaac

And don't understand why Ukrainians would fight an aggressor in the first place, because the only thing would be that more people would die....

It's simple

Option 1 - Long drawn out war, thousands dead, crippled by debt, economy run by the IMF, regime run by corrupt politicians in the pocket of lobbyists benefiting the corporations and immiserating the poor. Blue and yellow flag over the parliament.

Option 2 - Less long war, fewer dead, less crippled by debt, less in thrall to the IMF, regime run by corrupt politicians in the pocket of oligarchs benefiting the corporations and immiserating the poor. Blue, red and white flag over the parliament.

Option 2 has fewer dead. — Isaac

Then it's obvious nobody can make you understand the reality here. That Ukrainians will fight an imperialist aggressor, which in the end will likely lose just like it lost in the Russo-Japanese war or in Afghanistan.

Well, you convinced me to buy cryptocurrency (Bitcoin). We obviously are in the fear mode. Actually that might sound like a simple thing to do, but it isn't in real life: to know when the very bearish and when very bullish.

And I'm not going to be angry at you if (when?) the meager investment is -75% of the current price. :wink:

Putin's Russia has been and is in a (dehumanizing) systematic process of creating a Ukraine of more hate, which, in time, I'm sure they would/will use to justify more (given the chance), perhaps with the help of some questionable friends. — jorndoe

It's interesting that those neonazis don't get the focus of those seeing neonazis in Ukraine as Putin sees. But Putin's far-right views are in line with the imperialist idea of Russia being the third and final Rome... and everything good coming from Holy Russia and everything bad coming from the decadent immoral West.

From Putin's annexation speech (30th September):

Let’s answer some very simple questions for ourselves. I now want to return to what I said, I want to address all the citizens of the country – not only to those colleagues who are in the hall – to all the citizens of Russia: do we want to have, here, in our country, in Russia, parent number one, number two, number three instead of mom and dad – have they gone made out there? Do we really want perversions that lead to degradation and extinction to be imposed on children in our schools from the primary grades? To be drummed into them that there are various supposed genders besides women and men, and to be offered a sex change operation? Do we want all this for our country and our children? For us, all this is unacceptable, we have a different future, our own future

I repeat, the dictatorship of the Western elites is directed against all societies, including the peoples of the Western countries themselves. This is a challenge for everyone. Such a complete denial of man, the overthrow of faith and traditional values, the suppression of freedom acquiring the features of a “reverse religion” [the opposite of what the religion is] – outright Satanism. In the Sermon on the Mount, Jesus Christ, denouncing the false prophets, says: By their fruits you shall know them. And these poisonous fruits are already obvious to people – not only in our country, in all countries, including many people in the West itself.

Now trying to change the question again?

What in "as long as it takes - for the territory to be intact" do you not understand?

Anytime soon doesn't mean never, especially when you just said the US will back them up as long as it takes. And notice just what Milley says:

But Kherson and Kharkiv, physically, geographically, are relatively small compared to the whole, so that that -- the military task of militarily kicking the Russians physically out of Ukraine is a very difficult task. And it's not going to happen in the next couple of weeks unless the Russian army completely collapses, which is unlikely.

And this is quite in line what the Ukrainians are actually thinking about: Crimea is an issue for next summer. Or something on that timeline.

Incoherent ramble again from you, Isaac.

The fact that I stated is that Milley doesn't see a quick victory for Ukraine (just as the Ukrainians don't either see it) makes you fantasize that Milley (or your Miley) is concluding "that Ukraine are either quite unlikely or very unlikely to win back the territory they are aiming to regain." That's simply is utterly false.

Please look at what he actually said (from the site given):

(Milley) So, in terms of probability, the probability of a Ukrainian military victory defined as kicking the Russians out of all of Ukraine to include what they define or what the claim is Crimea, the probability of that happening anytime soon is not high, militarily. Politically, there may be a political solution where, politically, the Russians withdraw, that's possible. You want to negotiate from a position of strength. Russia right now is on its back.

The Russian military is suffering tremendously. Leaders have been, you know, their leadership is really hurting bad. They've lost a lot of causalities, killed and wounded. They've lost -- I won't go over exact numbers because they're classified, but they've lost a tremendous amount of their tanks and their infantry fighting vehicles. They've lost a lot of their fourth and fifth-generation fighters and helicopters and so on and so forth.

The Russian military is really hurting bad. So, you want to negotiate at a time when you're at your strength and your opponent is at weakness. And it's possible, maybe that there'll be a political solution. All I'm -- all I'm saying is there's a possibility for it. That's all I'm saying.

More of the timetable is actually discussed during the briefing.

And of course, the Ukrainians have put forward their terms, hence they are open for peace talks.

There are no correct moral claims. People only have incorrect opinions on what's good/bad, what should/shouldn't exist. — Leftist

How far postmodernism has taken us.

The fact that morality isn't totally similar as logic where things are either true or false and usually provable as so, yet this shouldn't really be any kind of problem for us. There is a link and it is studied in a branch of philosophy called ethics. So is the question...what?

So just to continue this thread. FTX went bankrupt with billions of missing.

Newly appointed FTX CEO John Ray III minced no words in a filing with the U.S. Bankruptcy Court for the District of Delaware, declaring that “in his 40 years of legal and restructuring experience,” he had never seen “such a complete failure of corporate controls and such a complete absence of trustworthy financial information as occurred here.”

Ray formerly served as CEO of Enron after the implosion of the energy titan.

So the guy who handled the Enron mess says this... :smirk:

Is it a trend that some the Super Bowl adds are for some new upstart companies a canary in the coal mine indicator (just notice what companies Super Bowl add is from my last comment above)?

Yet is the demise of FTX the bottom of the hype? Bitcoin is still more expensive than when this thread was started. And perhaps the hype is at least now over. Or then I'm wrong again and let's say the value of cryptocurrencies will go down another 75% or more. Likely people will want to forget it and hence the actual technology might really get into normal life.

Where in any of that does it say that Ukraine are likely to win back Crimea?

Nowhere. — Isaac

Wrong again, Isaac.

It's even in bold, so you could notice it. (But again, too much to assume you would read what people say or write)

we will continue to support Ukraine for as long as it takes to keep them free, sovereign, independent with their territory intact.

No, just the normal view. I cited General Mark Miley, — Isaac

LOL! :rofl:

An absolutely ludicrous idea!

Even you wrote his name wrong (MIlley), and obviously that when the general says the obvious, that there is no quick victory for Ukraine (something that Ukrainian military leaders themselves have said), you interpret in your fantasies "every single expert on the matter has concluded that Ukraine are either quite unlikely or very unlikely to win back the territory they are aiming to regain." How telling.

For others here, let's just quote what actually this Chairman of the Joint Chiefs has said, which obviously is very important. To have this thread to be about the reality about the war in Ukraine. From US defense.gov website:

This is a war of choice -- it's a war of choice for Russia. They embarked on a tremendous strategic mistake. They made a choice in February of this year to illegally invade a country that posed no threat to Russia. In making that choice, Russia established several objectives. They wanted to overthrow President Zelenskyy and his government. They wanted to secure access to the Black Sea. They wanted to capture Odessa. They wanted to seize all the way to the Dnipro River, pause, and then continue to attack all the way to the Carpathian Mountains.

In short, they wanted to overrun all of Ukraine, and they lost. They didn't achieve those objectives. They failed to achieve their strategic objectives and they are now failing to achieve their operational and tactical objectives.

Russia changed their war aims in March and beginning of April. Their war of choice then focused on the seizure of the Donbas, the Donetsk and Luhansk Oblasts. That was their operational objectives and they failed there. Then they changed again and expanded to seize Zaporizhzhia and Kherson.

The strategic reframing of their objectives, of their illegal invasion have all failed, every single one of them. And we've just witnessed last week Russia's retreat from Kherson. They retreated across the Dnipro River, they moved to more defensible positions south of the river. Their losses due to Ukrainian success and skill and bravery on the battlefield have been very, very significant.

And it's clear that the Russian will to fight does not match the Ukrainian will to fight. On the battlefield, Ukrainians' offensive up in Kharkiv has been very successful, where they crossed the Oskil River and they have moved to the east and are near the town of Svatove.

There is a significant ongoing fight down in Bakhmut right now and in the vicinity of Siversk and Soledar, where the Ukrainians are fighting a very, very successful mobile defense. There is limited contact right now in Zaporizhzhia and limited contact in and around the Zaporizhzhia Nuclear Power Plant. And as we already discussed, Kherson's offensive has already been successful.

So across the entire front line trace of some 900 or so kilometers, the Ukrainians have achieved success after success after success and the Russians have failed every single time. They've lost strategically, they've lost operationally, and I repeat, they lost tactically.

What they've tried to do, they failed at. They started this war and Russia can end this war. Russia can make another choice, and they could make a choice today, to end this war.

And what Milley continues about the Ukrainians:

Ukraine is going to continue to take the fight to the Russians. And I just had a significant conversation with my Ukrainian counterpart and he assures me that that is the future for Ukraine.

As Ukraine continues to fight, air defense capabilities are becoming critical for their future success. An integrated system -- an integrated air defense system, an integrated air and missile defense system, is what is necessary as Ukraine repels Russian aerial attacks.

And a significant portion of today's conversations in today's meeting with almost 50 countries focused on how we, as a global coalition, can provide the right mix of air defense systems and ammunition for Ukraine to continue its control of the skies and prevent the Russians from achieving air superiority.

To combat continued Russian strikes, last Thursday, the United States announced $400 million in additional commitments to support Ukraine, and those capabilities included missiles for the HAWK air defense systems, which is a complement to what Spain has recently committed. There's other air defense systems included in that $400 million package, along with ground systems such as up-armored Humvees, grenade launchers and additional HIMARS ammunition and lots of other pieces of equipment.

Wars are not fought by armies; they're fought by nations. This war is fought by the Ukrainian people, and it's fought by the Russian people, and this is a war that Russia's leadership has chosen to put Russia into. They didn't have to do this, but they did, and they have violated Ukrainian sovereignty and they violated territorial integrity of Ukraine. It is in complete contradiction to the basic rules that underlined the United Nations Charter established at the end of World War II. This is one of the most significant attempts to destroy the rules-based order that World War II was fought all about, and we, the United States are determined to continue to support Ukraine with the means to defend themselves for as long as it takes.

But at the end of the day, Ukraine will retain -- will remain a free and independent country with its territory intact. Russia could end this war today. Russia could put an end to it right now, but they won't. They're going to continue that fight. They're going to continue that fight into the winter as best we can tell, and we, the United States, on the direction of the president and the secretary of defense, we will continue to support Ukraine for as long as it takes to keep them free, sovereign, independent with their territory intact.

AND FURTHERMORE, Milley continues:

Ukrainians are not asking for anyone to fight for them. They don't want American soldiers, or British, or German, or French, or anybody else to fight for them. They will fight for themselves. All Ukraine is asking for is the means to fight, and we are determined to provide that means. Ukrainians will do this on their timeline, and until then, we will continue to support all the way for as long as it takes. It is evident to me and the contact group today that that is not only a U.S. position, but it is a position of all the nations that were there today. We will be there for as long as it takes to keep Ukraine free. Thank you, and I welcome your questions.

See reference here.