If you believe that if given infinite time you could count all the natural numbers, then you must also believe that if given infinite time you could count all integers by interleaving them (e.g. 0, 1, -1, 2, -2...) In that case, you have effectively counted all of the natural numbers twice. Counting all the naturals twice is equivalent of counting all the natural number to infinity, and then "afterward" doing it again.
I don't think you understand the concept of infinity
>>16923317Feel free to lick my butthole.
>>16923317>I don't think you understand the concept of infinitybecause, famously, there is a consensus on infinities. maybe you are lacking something?
>>16923317Sounds to me like he's discovering the concept of ordinal numbers and supertasks. I think you don't understand the concept of infinity.
>>16923314>If you believe that if given infinite time you could count all the natural numbersInfinite time doesn't grant you the ability to end an endless process, only to keep going indefinitely. You're retarded.
>>16923320>because, famously, there is a consensus on infinities. maybe you are lacking something?There is a mathematical or logico mathematical consensus about mathematical onfinity, but there is no consensus about philosophical infinity. The moment OP introduces some vague time concept (maybe the experience of time), he's leaving mathematics behind
>>16923343>There is a mathematical or logico(sp) mathematical consensus about mathematical onfinity(sp)oh good. then maybe you can tell me which is correct?[math]2^{\aleph_{0}}>\aleph_{1}[/math][math]2^{\aleph_{0}}=\aleph_{1}[/math]
>>16923314>infinitestopped reading there
>>16923314if given infinite time, you could count infinite numbers
>>16923353The answer is part of the mathematical consensus (there are models for both), but the philosophical problem of which axioms are "better" is of course open to debatehttps://books.google.com.co/books?id=Z9fJEYd8G94C&printsec=copyright
>>16923314You sound like you have more intuition about infinity than the people telling you "you don't understand infinity" have knowledge. Changing the order doesn't alter the cardinality, it's still [math]\aleph_{0}[/math] a countable infinity. What it does do is change the ordinality from [math]\omega[/math] to [math]\omega + \omega[/math]. Changing the order in which you enumerate the integers actually does change the "time" requirements from infinity to transfinite.
>>16923320Yes the consensus is that infinity doesn't end, so there in no count all in an infinite set since there is no all since all would require a final terminating value which doesn't exist in an infinite set.>>16923343No, infinity can be applied to time, its when you try to impose an end or finality to infinity that you start being incoherent, so he is saying that somehow time being unlimited means that other unlimited things will somehow be limited by time, but that doesn't make sense given they are both suppose to be unlimited. Its like saying the song that never ends will suddenly end if time becomes endless, its makes no sense because one's limited time is the limiting factor that prevents anyone from singing the song that never ends forever.
>>16923447for omega+omega don't you have to do 0,1,2,3,...,-1,-2,-3,...?
>>16923314The absence of infinity is a form of infinity. >If something can end forever, then infinity exists. >If it does not end forever, then infinity exists.
>>16923314>If you believe that if given infinite time you could count all the natural numbersWhy would I believe that?
>>16923583>Why would I believe that?Well, you damn well should. [math]\mathbb{N}[/math] is an infinitely large set comprised of finite numbers. Counting them is the same as applying the successor function over and over again. If we assume that you cannot count all of [math]\mathbb{N}[/math] even when given infinite steps, that means there must be at least one number in [math]\mathbb{N}[/math] that you would never reach. That means there must exist at least one finite number that you cannot reach by applying the successor function an infinite number of times. That is absurd and incorrect.
>>16923942What a silly statement Simple fact is if you want to count to infinity, any infinity, you will be counting forever. That's baked into the definition
>>16923314gor what fucking purpose? what would you get out of it? "philosophers" should be executed swear to god
>>16924105You've contradicted nothing I said. You are silly.
>>16924188Bro you're literally saying "you must be able to reach the end of small infinities eventually!"You're fucking retarded, stop breathing
>>16923314Yes, this is just a non-rigorous version of saying the set of all natural numbers is the same size as the set of all integers.
>>16924235Not only non-rigorous, but non-mathematical as well. There's no need to invoke time, it either complicates matters or oversimplifies the time concept
>>16924235I feel like he's saying something along the lines that the existence of transfinite ordinals are a logical necessity.
>>16924216Saying "if you count forever, there is no finite number that is beyond reach: all numbers are counted" is not the same as saying "you will finish." Your concept of infinity is pathetically weak.
>>16924324Finish... Finite... Hmm...
