With finite set there's a contradiction.You're missing the point. What has to be shown is that the fact that one can think of f(n) = n - 1 means that there exists one-to-one correspondence, or bijection, between N and N0. To do that, you have to show that f(n) = n - 1 is not a contradiction in terms. — Magnus Anderson
Suppose we have a hotel with a number of rooms equal to the number of natural numbers.
Suppose each room is occupied by a single guest.
That gives us a nice bijection between the set of guests and the set of hotel rooms.
R1 R2 R3 ...
G1 G2 G3 ...
Guest #1 ( G1 ) is in room #1 ( R1 ), guest #2 ( G2 ) in room #2 ( R2 ) and so on.
If there exists a bijection between N and N0, then it follows that we have a spare room for another guest. Let's call that guest G0.
---- R1 R2 R3 ...
G0 G1 G2 G3 ...
There is no longer a bijection between the two sets. G0 is not in any room. And if you try to add it to any room, you will either end up having two guests in a room ( not bijection ) or you will have to kick out one of the guests ( still not bijection. )
There's no way out of this conundrum . . . other than to pretend. — Magnus Anderson
The "custom of the land" as often corruption is referred to.It's about more than just politicians. Land. Universities. In any case, our original topic was the role of religion in political discourse, or the use of appeals to God/absolute truth in the political sphere. — BitconnectCarlos
It's not just Dedekind Infinity, it simply is Infinity in general. Galileo Galilei noticed the puzzling aspects of infinity a long time before Dedekind or Cantor (which in my view are best explained by the example of the Hilbert Hotel).The dispute concerns the notion of Dedekind Infinity. — sime
I think the term would be actual infinity that you should refer here to. Absolute Infinity is something totally else, which contradicts the Cantorian hierarchy of larger and larger infinities. Cantor simply preserved Absolute Infinity for God and as he was a deeply religious man, that shouldn't be overlooked. Yet for Absolute Infinity Cantor had no clue how to reason it.Recall that Hilbert believed that finitary proof methods could be used to ground the notion of absolute infinity that he considered to be indispensible for mathematics — sime
The incompleteness theorems didn't debunk actual infinity, what they debunked was Hilbert's aim to formalize mathematics and to prove its consistency and completeness by having a general answer (algorithm) to the Entscheidungsproblem. Mathematicians are usually just happy having infinity as an axiom in ZF and don't worry so much about it.and which the incompleteness theorems conclusively debunked — sime
If someone is willing to learn something, on the contrary.Cheers. Useful stuff. When someone makes such obvious mistakes, it's probably not worth giving detailed responses, because chances are they will not be able to recognise or understand the argument. The result will be interminable. — Banno
What makes you think so? Haven't you noticed that a lot of what the Trump administration does is performative. A lot of them are podcaster, newsanchors, social media-figures... even Trump made his name in showbizz. A lot of the time there's a 'show'-element to it.
I bet if Europe stands united together and doesn't blink first on Greenland, nothing happens. — ChatteringMonkey
If your politicians can be bought to play the tunes of foreigners, which especially now they surely can be (starting now from Trump himself), you should blame your own people, not the foreigners for this.It's the foreigners who buy up large plots of land and make large donations to politicians and universities. Everyone notices the poor foreigner; the rich are more subtle but far more dangerous. — BitconnectCarlos
You might be right on this, which makes me sad if it happens. :sad:Well, it's definitely happening. — Tzeentch
Oh, he is really willing to do it. He needs Greenland, he needs to expand the territory of the US.I think he understands more that you give him credit for. I think he sees everything as a negotiation to get the best deal... that's why he never rules anything out. If you rule out military action for Greenland then that is something you cannot leverage to bargain for it. That doesn't mean he is willing to do it. — ChatteringMonkey
Sorry Magnus, but this what you say is wrong::lol:
— Banno
For a grownup man, that's a pretty childish response. — Magnus Anderson
A bijection does mean that sets can be put into a one-to-one correspondence.That a bijective function exists, cretin, does not mean that the two sets can be put into a one-to-one correspondence. — Magnus Anderson
No. There are injections and surjections, which aren't bijections (both injection and a surjection) and they are also called functions.If the word "function" is defined the way mathematicians define it, namely, as a relation between two sets where each element from the first set is paired with exactly one element from the second then, if a bijective function... — Magnus Anderson
I'm not sure if Trump understands that American power comes from the alliances it enjoys. I think he truly believes that US alliance with Europe has been only a financial burden without anything gotten back. He has stated this so many times, just like in his own mind the EU was formed to be against the US, again a totally bogus historical reason. He also has said so many times that "If we would need them, they wouldn't come", which just goes against history as the US did get help in Afghanistan the only time article 5 was used (after the 9/11 attacks).But I don't think he wants to push it that far that the US effectively loses all its allies, because that is part of what makes the US so powerfull. — ChatteringMonkey

Latest interview starts really hinting on that. The easy or the hard way. This is bad.He could do that and might do that — ChatteringMonkey
Then the damage has already been done. NATO has already been done and the US has been seen as a threat itself. And how humiliating is it then give back US territory ...assuming there are MAGA-lunatics still around in US politics?After his term, the next administration would have to affirm their willingness to enforce it over and over, — ChatteringMonkey
Does he, really? Does his base really want the US to be in NATO? Does his base think it's important to have good relations with those puny Europeans? No, they will just cheer for their President to have the audacity to do what he wants. He will surely have his "base", no matter how small it is.And 2) he does still have to consider his political base somewhat. — ChatteringMonkey
First, Europe should play hard.So like I said in my first post here, whether or not they turn over Greenland will probably also depend on how much economic pain Europe is willing to accept for it, if the US wants to play it that hard that is. — ChatteringMonkey

Well, that morphs into a Trump thread, because there's always 'Recent geopolitical developments'... just as there will be the US president and his policy actions debated.perhaps it would be good to combine all these threads into a 'Recent geopolitical developments' thread, or something like that. A mod might be able to help with that, if you like the idea. — Tzeentch
One note to the discussion that you and @I like sushi are having: the political discourse is obviously quite different between the continents, but the actual government spending is quite the same. Which is quite surprising as the US doesn't have universal health care etc. Even if the US usually denies it and thinks the European countries are the "welfare nanny-states", the similarities are obvious.And yet there's still little in the way of socialism in Europe. That's because the EU controls economic policy, and it's firmly neo-liberal. Again, what you're pointing to as evidence of European leftism is just government handouts in an otherwise liberal domain. — frank


In Germany in 2024 about 40% of the electricity was produced by renewable energy. Then a large share comes from coal, which it get's from Poland.Germany is the most important one, 'the economic engine' of Europe. — ChatteringMonkey
Never underestimate the impact of the economy, as these tensions flare up in economically distressed areas. There's a lot of foreigners in Mayfair and other posh sites in Central London with a lot of foreigners, but .It's not just a questionable effect on the economy. The British grooming scandal wasn't economical. There are real concerns with male immigrants from countries with institutionalized misogyny. — RogueAI
What immigrant group are you talking about acting this way? Americans in Latin America or what? I think you confuse those vocal people speaking on the behalf of immigrants, when it comes to Western countries.What of immigrant groups that claim to possess absolute truth and consider it their prerogative to spread or impose it on the native population? — BitconnectCarlos
First of all, nobody's replacing anybody.The Great Replacement exists in a quantum state.
If you say that the Great Replacement is real, but is a good thing, then this is an argument that is allowed to be taken seriously and given real credence.
But if you say that the Great Replacement is real, but is a bad thing, then that is dismissed as a racist conspriacy theory which is beneath rational discussion.
The exisence of the phenomenon as a statistical fact is subject to epistemic uncertainty a lot like Shrodinger's Cat until the moral evaluation is brought forward to frame it, thus collapsing the waveform. Only once the speaker's morality is observed do their statistical facts become distinguishable as reality or conspiracy theory.
In this way, the fact of the existence of the Great Replacement is determined, not by statistics, but by moral evaluation and rhetorical framing.
That aspect of the Left's argument on this is utter bullshit. Settle whether it's happening or not first, which should be strictly based on the data, before we go evaluating it as good or bad or neutral.
Here's the thing on the demographic shift: I am perfectly happy to replace certain categories of whites whom I don't like with browns. — BenMcLean
It's not about helping "to build a civilization", it's about helping your society, your civilization.I'm OK with bringing in non-whites as long as they are the kind of non-whites who are going to help build a civilization and not the kind who are going to tear one down.
But fundamentally, completely apart from any ideology which says there's anything particularly special or superior about whites, absolutely nobody should be expected to just accept a system which is deliberately, maliciously stomping on their people's faces, no matter what color they are, no matter what period of history it is and no matter whether academic elites say they get to count as "historically marginalized" or not. — BenMcLean
The American right should understand that Trump is the real RINO and his populism is extremely toxic and destructive for the right. It just leans on the worst aspects of what the right has been about.I am just hoping that the new American Right after Trump can be one which still promotes liberty and justice for all -- and to do that, it's going to need a new political theory, beyond Trump's populism. — BenMcLean
Who are the real dunces in this story? — ChatteringMonkey
Nothing as it simply doesn't make sense. It's all about the flag waving on the island. It's that Trump can say that he made the US greater in size with a territory larger than Alaska. It's make America Great, literally.Statements from House Trump and Ogles don't make much sense. What's missing? — jorndoe
Too simplistic. All Great Powers have had quite different foreign policies toward different states.That doesn't sound different at all. That's US foreign policy in a nutshell. — Tzeentch
Well, only a minority supports the Venezuela campaign in the US.I'm going to go out on a limb here and say it's because Washington doesn't give a flying fuck about what the American people think. — Tzeentch
WASHINGTON, Jan 5 (Reuters) - One in three Americans approves of the U.S. military strike on Venezuela that toppled the country's president and 72% worry the U.S. will become too involved in the South American country, according to a Reuters/Ipsos poll that concluded on Monday.
Well, this actually varies by country and do remember the change in energy production happening now. For example France gets a huge share of it's power needs from nuclear energy and my country gets 90% of it's electricity from nuclear power and renewable energy. Oil isn't so dominant as it was during the 1970's.LNG, the US is our main LNG supplier, which replaced the Russian pipeline gas. And also oil. — ChatteringMonkey
I'd still call more accurately the Donroe doctrine, because Trump's moves are totally different from anything else we've seen. It's basically "we've got this awesome military, so we can plunder weaker countries.".- The US is showing clear commitment to enforcing the Monroe Doctrine (aka domination of the western hemisphere). — Tzeentch
Good that you notice the irony, because the US itself made this alliance and was truly successful of creating an alliance system that the Europeans voluntarily and happily were in, and thus gave US a say in their defense policies and also gave a lot of economic perks to the US (starting from the dollar being the reserve currency, even after Nixon's default).- The US views Europe as an unreliable ally in the long run (ironic, I know), and a potential rival. — Tzeentch
Actually, it's really about the map and territory. Trump wants Greenland and then perhaps Canada, because then the US would be the largest country in the World. Even with Greenland, that's the largest territory extension for a while in US history, because it's larger than Alaska.- Greenland comes with large territorial and economic claims on the Arctic. — Tzeentch
In case of US-EU, the Russians hardly don't matter anymore.- In the case of a US-EU split, Greenland would serve as a forward base against the Russians (mainland Europe could no longer function as a bridgehead). — Tzeentch
Defense procurement is long term thing. And that's why something like SAFE does tell a lot.Europeans are a bit shocked at the moment about it all, but will slowly come to the realisation that they really don't have anywhere else to go in the short term. — ChatteringMonkey
Is there for Trump so much? If he get Greenland and the cost is NATO, why would it be for him a problem? Let's remember that this guy truly thinks that it's a great idea to go to Venezuela and take their oil and the US has been cheated by it's allies.I don't think there will be a military conflict over Greenland in any case, to much is at stake for both parties — ChatteringMonkey
I'm not sure what you refer on energy, because the US doesn't export much. With digital services, Europe is starting to be aware just how dependent they are on US tech. Basically the real issue here is that the US is an untrustworthy ally, and is capable of freezing the essential logistics and supplies of advanced weapons systems. This is one of the reason why the heated F-35 vs Gripen discourse in Canada, for example.as the US is the main energy and digital services provider etc, — ChatteringMonkey
Actually, let's be a bit more specific about just how it went: The US Military, on it's own and without the politicians in Washington, actually basically destroyed Al Qaeda in Iraq and it's grasp in the Sunni areas by the Sunni Awakening, where Sunni tribes were supported to fight Al Qaeda and helped to form the Sons of Iraq.Destroying the Ba'ath Party in Iraq left a vacuum which created the conditions for ISIS. — ChatteringMonkey
Which doesn't make sense. How is this even be thought to work in a country that basically is very close to just collapsing into anarchy? And why would the Chavistas roll over?In Venezuela they left the regime intact... minus Maduro. — ChatteringMonkey
Venezuela’s interim leader, Delcy Rodriguez, has said that “no foreign agent” is running Venezuela in the wake of Nicolas Maduro’s abduction by United States military forces.
Rodriguez, who had been Maduro’s vice president before his abduction, spoke during a televised event on Tuesday, a day after Maduro and his wife, Cilia Flores, pleaded not guilty in a New York court to drug-trafficking conspiracy charges.“The government of Venezuela is in charge in our country, and no one else. There is no foreign agent governing Venezuela,” Rodriguez said.
In decades we will have actual history writing. And when it comes to Trump, it really can be things like he got pissed off about Maduro dancing and ridiculing him. Just like that one partly reason for the Soviet Union collapsing was that Gorbachev and Yeltsin didn't get along (and the people doing the Putsch didn't get Yeltsin).In 20 years we'll learn there was some of angle that was conveniently left out of the discussion, like the Israel angle with Iraq, that also 'happens to' establish mens rea. — Tzeentch
The Trump administration is quite different from the Obama administration, just as Putin is different from Yeltsin, even if the former are US administrations and the latter Russian administrations.They are just playing dumb, attributing to incompetence what ought to be attributed to malice, and attributing to the Trump administration what ought to be attributed to the machinations of all of Washington and the foreign policy blob. — Tzeentch
I think the apt name is Donroe doctrine. Very different from the doctrine that European colonizers shouldn't try to take back their colonies that they've lost. (Which btw. was shown to be an empty threat in the late 19th Century, when France attempted to take over Mexico and had it's debacle there. But then the US wasn't a Great Power yet.)It's clear the American goal was to send a signal to all of Latin America: If you get too cozy with other great powers, we have the power and the will to ruin your country overnight. It's the Monroe Doctrine. — Tzeentch

I think that Saddam Hussein was responsible for a lot more of suffering and death than the previous busdriver then President Maduro ever did. Saddam's policies were even worse for Iraq. Hence there were similar arguments for intervention in Iraq. You have always these kinds of arguments and the neocons have stated these, even if the real cause has always been the threat that the country poses.All that said, Maduro was responsible for a huge amount of suffering and economic degradation. Venezuelans have been reduced to living in poverty while he and his cronies squirrelled away the wealth of the nation in their private accounts. His wife owns entire neighborhoods in Caracas according to reports. — Wayfarer
:up: :100:I’m constantly reminded that I give Trump and his idiots too much intellectual credit for decisions, when in reality most of them are just a bunch of absolute morons representing the most brainless slobs of meat walking this earth. — Christoffer
Do notice one aspect here: everybody in the US Foreign Policy sphere, which obviously includes the Brookings Institute, is now walking on egg shells. Criticism will get a nasty attack from the White House, but there is still criticism.but from a team of 12 experts I would expect more - especially given the annual funding Brookings receives. — Tzeentch
Focusing narrowly on oil access or prioritizing creditor repayment over recovery would risk creating a small set of rent-seekers while keeping Venezuela’s failed institutions largely intact.
He seems to believe that oil revenues will fund the ongoing presence, stating that, “We’ll be selling large amounts of oil to other countries,” and that running Venezuela “won’t cost us anything.”
This is nonsense.
The oil industry in Venezuela is a shambles.
Trump’s particular brand of lawless bravado, narrow-minded nationalism and crony capitalism have combined in Venezuela to lead our nation down a dark hole of open-ended responsibilities for the world’s largest holder of oil reserves and the region’s largest source of migrants (though not narcotics, the alleged threat). The harmful consequences for U.S. national security, and international peace and security more broadly, will unspool for years to come.
Trump’s ‘Donroe Doctrine‘—his rebranding of the Monroe Doctrine aimed at building a U.S. sphere of influence in Central and South America—seems to have made a relatively secure region meaningfully less stable overnight.
These "adults in the room" aren't adults in the room, as in Trump's first administration. Only vaguely Marco Rubio tries to give an impression of normalcy by trying to say that the operation was to bring into justice Maduro, that the US isn't at war with Venezuela, yet his POTUS quickly made it clear it was about the Venezuelan oil reserves and that the US taking over the country.It looks like "adults in the room" are betting on VP Rodriguez being more pliant and reasonable than her (former) boss. So, to them, "running the country" is basically keeping Rodriguez as a technical president and trying to work with (strong-arm) her. From what I have picked up about Rodriguez, she seems like a competent technocrat. But how secure her position in the hierarchy is an open question. — SophistiCat
The political opposition to Trump hasn't woken up to the fact that this isn't a normal President playing by the rules. Many are just dumbstruck. And then there's the vast majority who don't follow politics and get only mad when the US economy tanks... or more precisely their own economy tanks.I still don’t understand how far he can go before those with the power to remove him, do so. How many illegal things has he done by now? What does it take for the US to remove a president? Impeachment doesn’t work if the people who decide on it are part of his cult. — Christoffer
The Parties undertake, as set forth in the Charter of the United Nations, to settle any international dispute in which they may be involved by peaceful means in such a manner that international peace and security and justice are not endangered, and to refrain in their international relations from the threat or use of force in any manner inconsistent with the purposes of the United Nations.
I think you are correct. Just look how problematic ultimates like infinity are still in math and logic.Maybe the word ultimate is the problem. — Tom Storm

A lot more worse.Venezuela was already a failed state. How much worse could it get? — frank
How much of that Iraqi oil went to US oil companies in the end? Not much, there's few of them, but they don't represent the majority of the foreign companies now in Iraq: there's Russia, China, the Europeans etc.I liked the rest of your observations about the oil situation. — Tzeentch
Sorry, I didn't understand this part.When I say I believe the universe is fundamentally good I am merely the superiority of a FAITH in truth and the ultimate goodness of the universe with the inferior FAITH in some book that has a talking serpent and a talking donkey. They are both types of faith. — Art48
Just what institutions I ask? In his press conference, Trump mentioned oil 20 times while he didn't mention drugs, war on drugs or democracy at all. That's quite telling just what "institutions" the sick fuck is values.Trump is just “defending our institutions”. — NOS4A2
Lol, Trump threw Maria Machado immediately under the bus, didn't even bother to mention Edmundo Gonzales, but was eager to tell that they were in contact with Maduro's vice president Delcy Rodriguez.And it probably hurts knowing that the exiled opposition leader in Venezuela dedicated her Nobel peace prize to your favorite president last year, isn’t that so? — NOS4A2
Actually, I don't. And neither do you.Now you know. — NOS4A2
You are just contradicting yourself. So now you are in favor of nation building?and your high-horse leaders just sat around and let him repress his citizens, as they’ve done all over the world. So much for “defending our institutions”. — NOS4A2
To break the Atlantic tie between the US and Europe, just as to hinder the European Union has been a plan of Russia for a long time. So the Russians are quite honest when they say that Trump's plan matches their plans. This is a dream come true for the Kremlin.Whose plan is it?
The way I understand it, Putin, Xi JInping and Trump are in a quid pro quo threesome, each concerned with their own imperialist goals. — Questioner
Whose power play is this?I concede that maybe I shouldn't have used the world "superpower" to describe Russia. Maybe "power at play" would have been more accurate. — Questioner
