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B
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Comments by "B" (@user-pr6ed3ri2k) on "How An Infinite Hotel Ran Out Of Room" video.

@ChayaKhy um, no. well actually yes if you do it a finite amount of times then it will only be guaranteed different for the first n things in the list where n is the number of times but if you do it infinitely many times it will guarantee that it isn't the same to the first ω numbers so uh yeah you just didn't understand it maybe try understanding something that has been shown true provably many years ago before claiming that it's nonsense?
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@ChayaKhy also the letters after the letter you flipped aren't defined yet, you just have a finite string for now so no in fact, if you use the exact definition used in the video, it will never be the same as any part on the list that's just a technicality though, but even if you ignore it it still proves you wrong.
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@Ανλάκι Λουκ um thats not the definition of infinity infinity just means neverending not contain everything
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@robotnoir5299 to first paragraph: if it's physically impossible irl doesn't mean it isn't possible in theoretical math land. like, if math was based on reality, why would we even be talking about infinite hotels in the first place? to 2nd paragraph, yeah, i think you're embarrassed for a different reason now. to 3rd: their names are unique and infinite, ABBA is just the nickname for ABBAAAAAAAAA... in this situation but it also could be for ABBAAAAAAAAAAAAAAAAAAABAAAAAAAAAA... as well.
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@milesaway000 the list isn't finite.
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@robotnoir5299 yes, you can IMAGINE robots that do the thing, but as long as you haven't proven that it CAN do the thing using the mathematical ruleset, no1cares about the robot.
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@Ανλάκι Λουκ "that something "infinite" has limits but he is deadly wrong" seriously? you don't understand something that has been proven YEARS AGO and say that it's the rest of mathematics that's wrong? 10/10 dunning kruger effect "i'm right and all of you are wrong because reasons"
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@Ανλάκι Λουκ also, you should probably like, NOT say things like "don't know who on the mathematics world though that something "infinite" has limits but he is deadly wrong" to well known accepted proofs? just because you think they are wrong doesn't mean they ARE wrong. it just sounds like someone saying I AM RIGHT AND ALL OF YOU ARE WRONG BECAUSE REASONS™!
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@Ανλάκι Λουκ there are infinite numbers of naturals, yes. specifically ℵ_0 of them. and there are 2^ℵ_0 of reals and infinite binary A and B strings. the problem with your argument is, there are different kinds of infinity.
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@robotnoir5299 1. no and i don't really get the analogy + you deleted your comment after i gave a response to that 2. the hotel is an analogy. we don't have to know how it was built, why no one wants to speak to the manager, etc. + again, real life doesn't limit math. + "many hotel guests had to walk an infinite distance " room number infinity doesn't exist since infinity isn't a number. + 3. we don't need to believe that, the hotel is an analogy for an actual mathematical concept and doesn't need to exist. " But if I ask you to sort a few infinite numbers" there is no such thing as an infinite number. + you'll just get some weird looks around the room because people are confused as to how that is a legitimate non troll question. + "Can't we just ask the tradies how they sorted your numbers before sticking them on your hotel doors how they did it, and do that again?' you can't, because the hotel is an analogy. those people don't exist (what's a "tradies"? i dont know much english)
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@milesaway000 "infinity is beyond everyone's comprehension" um, sorry but, isn't it just you?
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@robotnoir5299 it doesn't matter if the real world is limited by these limits. It's math, math is a fundamental, unchanging concept of the human thought, and the human thought, or imagination, is famously known for normally not being compatible with reality.
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@Ανλάκι Λουκ uh, the naturals are every integer after -1 or 0 depennding on your definition, yet infinity is not a number. so the naturals aren't infinite?
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@Ανλάκι Λουκ there is one sequence not in the list because the way you listed them was incomplete.
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@Ανλάκι Λουκ wait a minute, i just reread your comment and i can think of a few counterexamples already, they're literally just the naturals and reals with no 0 included. they don't contain everything, therefore they are not infinite?
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@Ανλάκι Λουκ in this case ℵ_0 (the size of the 1, 2, 3, 4, 5, ... set) happens to be less than 2^ℵ_0 (list of all INFINITE binary strings). who would've thought, 2^cardinal is a bigger cardinal!
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@Ανλάκι Λουκ the problem with your argument is that the 2 lists of names are absolutely irrelevant. there's only 1 list, and it includes both A and B names.
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@Ανλάκι Λουκ it's weird how you say the comparison is irrelevant, then give an even more irrelevant example and claiming that it is relevant.
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@Ανλάκι Λουκ if you can't understand basic cardinals, and insist that you are right and everyone correcting you is wrong, there is nothing i can do about that. aside from, you know, sending the suggestion of rewatching the video or reading the wikipedia article? unless you also have an irrational hatred of wikipedia, which in that case, just watch the video.
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@robotnoir5299 cardinal math isn't based on reality, it's based on abstract, fundamental concepts that don't care about your opinion which can be turned into analogies that also don't care about reality + your opinion. (wow, a time in youtube where saying "your opinion is irrelevant" is valid. )
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@robotnoir5299 the math can represent things in reality, but things in math dont already represent things in reality
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@robotnoir5299 i agree with first part
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what's with this thread attracting all sorts of uneducated people who think that the video is nonsense because me cannot understand :(((((?
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@fall4sleepfall4sleep26 if the logic tells you one is bigger, then it IS bigger! math is based on logic! i genuinely can't understand what your problem is! also, infinity CAN have a start and end. imagine the numbers between 0 and 1 including 0 and 1. what's the start and end? that's right. 0 and 1! but the problem is, there are infinitely many numbers between 0 and 1, so, you can give an end and start to infinity!
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@robotnoir5299 just thought of more examples: can these exist?: negative numbers non integer real numbers pi the fundamental concept of multiplication and division polynomials sin(x) or the other trig functions literally any function from non integers to non integers cardinals like N_0 e the set of naturals (it's infinitely large, no?) literally any set (possibly representable as boxes, but infinite sets and sets with elements you can't represent exist so yh) quaternions the elementary operations of arithmetic aside from addition subtraction when you try to solve number - bigger number zero (is it possible to represent 0 of anything using a physical object?) open sets dense sets like the rationals the concept(s) of "countably infinite" and "uncountably infinite" the most basic examples i could list
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@robotnoir5299 congrats robot noir, you just showed your absolute incapability of understanding the video made by ted ed. good job. everyone's laughing clapping for you now.
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@robotnoir5299 also i just read the part about binaries, and that just makes it worse. ABBA is just a nickname for ABBAAAAAAAAAAAAAA... and if you were to turn that into binary with your method, that would become 011000000000..., and since every sequence will result in an infinite number (aside from AAAAAA..., but that's the only exception) and since they are all the same infinity, they'd all be in room "number" end-of-the-number-line (which doesn't exist, as you can always just add 1 to a number on the number line to get an even bigger one. )
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@ChayaKhy ah crap i don't really remember much about this but you can imagine it as the length of the list (wait, isn't that exactly what we were talking about before?) and you can see normally that the powerset (ez way to generate list of 2^x things from list of x things) has more elements than the original set (that's a rule of powersets) so it now make a bit of sense that it would continue for the infinite sizes (ℵ_0 should be less than 2^ℵ_0, right?)(aleph 0 is the accepted term for the "size" of the natural numbers)(also there's no simpler term for 2^ℵ_0 because the statement that that equals ℵ_1, aka there's no such thing as a size between 2^ℵ_0 which is ℵ_1 and ℵ_0 is the continuum hypothesis (also, 2^ℵ_0 is the cardinality or "size" of the real numbers (imagine the abba sequences as binary like abba would be 0110000000... and then add a 0. at the start (0.01100000... ) nice, that happens to be a list of all numbers between 0 and 1, but in binary now convert that to decimal (0.375000000000000000... or 3/8) now you have the normal way of listing numbers 0<=x<=1 now notice that the actual reals should have same size as ℵ_0*2^ℵ_0 (all the numbers are of that same form except you have an integer at the start, and ℵ_0 is the definition of the size of the ints) and since big infinity absorb smol infinity when multiply, the size of the real is 2^ℵ_0)) why have i gone on rambling about mathematics sorry
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@robotnoir5299 @robot noir new1stpara: ok, are numbers a physical thing in reality? no wait don't answer that, philosophy sucks new2ndpart: idk new3rdpart: um, there is a correct answer, and that answer was made from the zfc axioms + endlessness is a possible concept. if it wasn't, why would we even have a word for it? to last part: uh, the hotel is just an analogy, it's just supposed to be a intuitive way to understand cardinality assuming that everything is idealized, and there are no karens, and they can switch rooms in precisely 0 seconds, and that no one destroys the whole place, etc.
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@robotnoir5299 also, the axioms were designed to be as reasonable as possible. I can list them here in oversimplified form: 1. 2 sets are equal iff (if and only if) they have the same elements (axiom of extensionality) 2. a set doesn't have infinite nested sets. (axiom of foundation) 3. set builder only used to define a certain subset of a set. if you don't have this, you'll get that weird error when you make the set of all sets that don't contain themselves and the set of everything. (axiom schema of restricted comprehension)(axiom 2 also prevents paradoxes)(schema because set builder can have many different predicates an inputs) 4. if you have 2 sets, x and y, the set that contains both x and y exists. (axiom of pairing) 5. the set you get from grouping all the members of the members of a set (this set has only sets as members and those sets have sets)(basically a nested set) exists. (axiom of union) 6. the set of all outputs of a function f(x) that you can define exists. (axiom schema of replacement)(schema because there are many different kinds of f(x) (obviously)) 7. there exists a set X with infinitely many unique members (example: {1, 2, 3, ...}) (axiom of infinity) 8. the powerset of a set exists. (take a set, make a set of all sets that are like the original set except missing or not missing some of the elements)(the party bus in the video is equivalent to the numbers between zero and 1 in size which is equivalent to the powerset of naturals (the room numbers; {1, 2, 3, ...}) in size. ) (axiom of powerset) thats standard 8 in zf zfc has a ninth one 9. for all sets R, there is some binary relation X (like a < x, only compares 2 elements) that well-orders R. (well-ordering theorem)
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@robotnoir5299 your comment just committed gone
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@ChayaKhy um your welcome i guess
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@milesaway000 why did you edit your comment to make it sound less about a question and more like a mentally unhinged person wrote it?
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@milesaway000 what just happened to the @ it got turned into randomness doesnt really matter but still
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nvm it got fixed
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@milesaway000 your 2nd comment committed gone too
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@Ανλάκι Λουκ it's common sense? IT'S COMMON SENSE? THE NATURALS DON'T CONTAIN EVERY NUMBER IN THE REALS, THEREFORE THEY AREN'T INFINITE?
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@Ανλάκι Λουκ im sorry for responding rudely, i just get extremely triggered when dunning kruger effect because reasons as well
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@Ανλάκι Λουκ also, the only comparisons of infinity here is from the set of all finite numbers and the set of all infinite binary strings. infinite set of names contains every name obviously, but it's irrelevant to the video.
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@Ανλάκι Λουκ your argument is the perfect example of dunning kruger and irrelevant conclusion.
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@robotnoir5299 please, just try to understand math more instead of saying words that appear to contradict the math and shows that everyone aside from you is ✨confused✨when in reality you're the ✨✨confused✨✨one and is self projecting onto others.
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@robotnoir5299 youtube deletes comments right after making (the illusion of a visible comment only appears to your screen and reloading instantly fixes it)
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@robotnoir5299 "so they removed my irrefutable comment" yeah, im not so sure about that
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@robotnoir5299 oh ok so thats what a tradie is
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@robotnoir5299 the request to sort infinite names isnt an analogy because what the heck is it an analogy of?
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@robotnoir5299 to the last part, um, yeah i guess thats a fair point
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@robotnoir5299 also it doesnt matter if something in math doesnt happen in reality, its math + we decide the rules for math, therefore there is in fact a correct answer to a good amount of math problems (ofc, there is 2^n_0 =?= n_1, but most math problems that we need to solve arent of the unsolvable kind)
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@robotnoir5299 its more like spiderman vs electro (yes i dont remember any other fight im sorry) where we know who will win because the movie (analogy for the rules of math) say so
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@robotnoir5299 on 2nd read, uh, no. there's this misinformation breeding zone called reddit where you can post things uncensored. no one will erase your words there so i dont agree with the 2nd part.
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+ you cant prove that you didnt delete your comment
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@fall4sleepfall4sleep26 that moment when you dont understand transfinity and assume that we are assuming infinity is an absolute 💀 anyways by definition, no, the hotel can have "all" rooms filled with guests yet have free space left because there is always a spot for a guest to move to, not because there is always a spare room. "make one infinity bigger" we're talking about cardinals, not infinity, and there is something bigger than ℵ_0, 2 things actually, ℵ_1, and 2^ℵ_0. please at least try to understand the basics of cardinals first before commenting about how "there is a problem" when there is none.
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@fall4sleepfall4sleep26 its not facts, it's what you specifically think. you are just projecting yourself onto others and think that everyone else is also using their opinion.
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@thatgoldenguy3272 💪👍👍👍
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@fall4sleepfall4sleep26 um, what you just described is perfectly valid? i dont understand your point? its true that if you try to destroy n_1 with n_0 then n_1 will still be n_1 because it makes n_0 basically 0 to it?
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@fall4sleepfall4sleep26 same with 2^n_0... i dont see any sarcasm? this is valid math?
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@fall4sleepfall4sleep26 um, your infinity isn't infinity, it's called a cardinal, that is definitely not the same as infinity my cardinal (n_0) is incomparable to your cardinal (n_1 or 2^n_0, your pick) + there are no numbers here, you can't represent any of these in numbers
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@fall4sleepfall4sleep26 um, actually, the whole mathematics community is the one who decides what cardinal means. you are the arrogant one. I am giving you a commonly accepted definition, yet you replace it with your own definition that you made up and are calling everyone else "arrogant" for not using your definition. you just want me to close my browser because you can't make up an excuse to hide your arrogance. also, cardinals, again, are NOT infinity.
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@fall4sleepfall4sleep26 also again, 2^N_0 isn't a thing with next numbers, it's a continuum, there's no such thing as next in 2^N_0. there may be a next in N_0, but not 2^N_0, and it's unsolvable if there is a next in N_1.
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@fall4sleepfall4sleep26 "because my infinity will have always a next number no matter how much you have. " that's true! i agree with you! your infinity is aleph 1 or powerset aleph 0, and mine is just normal aleph 0, so of course your infinity is bigger! when did i say that it is not bigger?
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@fall4sleepfall4sleep26 also, you're a human too, so aren't YOU arrogant as well?
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@fall4sleepfall4sleep26 it doesn't matter if it isn't a real problem, it's math, math doesn't have to be limited by the real world.
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@fall4sleepfall4sleep26 that's... not true... math isn't just for understanding things, it's basically for inventing bunch of axioms and see what ways that will make you help understand the world
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@fall4sleepfall4sleep26 yes, infinity doesn't care if one could be bigger, because none can be bigger, but the problem is, N_0 isn't infinity.
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@fall4sleepfall4sleep26 2^N_0 isn't infinity, N_1 isn't infinity... the list goes on
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@fall4sleepfall4sleep26 they're just called "cardinals" for a reason.
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@fall4sleepfall4sleep26 uh, there is no such thing as a start and end to infinity, it's a concept, not a mathematical object also, one is bigger, powerset aleph null is bigger, and i have proof of that lets say you have powerset n0 and n0 in a list: N_0 2^N_0 1 AABAAABABBBABA... 2 BABBAAABABABAB... 3 BBAAABABABAAAB... 4 BABABABAAAABAB... 5 AAAABAAAABAAAA... ... ... of course, it doesn't matter how 2^N_0 is ordered because you can't list it out. next, get the first letter of the first word, 2nd of the 2nd word, third of the third word, and so on, and make a new word that has all those letters in the same place but flipped, then boom, you have even more words in 2^N_0 than N_0. tell me, how can you say that N_0 is bigger than 2^N_0?
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@fall4sleepfall4sleep26 they are NOT infinity, how many times do i have to repeat this?
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@fall4sleepfall4sleep26 dude, just saying "you can't compare 2 infinites", you need to PROVE it. cardinals are DEFINED USING ZFC, we don't have to make rules up since the word "cardinal" in math only makes sense if we use ZFC
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@fall4sleepfall4sleep26 math is not from nature, so it doesn't matter if you can't compare infinity in nature, it's math after all!
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@fall4sleepfall4sleep26 how do you push an argument to infinity?
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@fall4sleepfall4sleep26 "infinite" and "infinity" are not the same in math. NOT. because N_0 is NOT infinity, it's a CARDINAL, yes, read that, CARDINAL. if it was infinity, then why could things like 2^N_0 exist? that's right, it's because it ISN'T INFINITY.
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@fall4sleepfall4sleep26 tl;dr just because you make up the rules doesn't mean your logic is automatically more valid than the logic people who actually have a brain spent years making
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@fall4sleepfall4sleep26 dude, the video we're on and the comment i posted is absolute proof that one "infinity"(really a cardinal) (2^N_0) is bigger than another "infinity"(also a cardinal) (N_0) also, why are you ignoring my comments? you literally only responded to the one about arrogance and not to the ones about actual math, so I'll leave this one reply that you have to respond to because you keep ignoring the rest of my comments.
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@ПавелПовх-з3у there is no addition involved here. proven how? if you try to prove it with addition, there will always be 1 more to add, so that's no good. but trying to prove it using 1 to 1 comparisons shows that 2^N_0 is in fact > N_0.
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@ПавелПовх-з3у also, why is knowing and being told that it's infinite different?
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@fall4sleepfall4sleep26 " my words but he keeps trying to convince me. and i just love him trying so hard" that moment when you commit arrogant :skull:
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@OsuKaylan i want to mush my brains though, it's literally the only thing i am even half good at
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@fall4sleepfall4sleep26 i get it now, you don't want to respond to most of my comments. because if you did, you would know why you are irrefutably wrong. what's with most arguments on youtube ending with someone pointing out that the other can't accept defeat?
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@ПавелПовх-з3у it's because it isn't. adding 1 letter isn't how the weird names are generated, it's adding INFINITELY MANY letters, INFINITELY MANY times. infinity^2. not really a precise proof, but you get the idea.
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@ПавелПовх-з3у (the size is actually 2^N_0 but "N_0^2" is good enough)
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@ПавелПовх-з3у who defines where first infinity ends? the mathematics community, of course! there's a wikipedia article about it, you should probably read it if you want to know about cardinals! also there is nothing inbetween N_0 and N_1, and there is no such thing as 1/N_0 because what on earth does that even mean? there's no number which you can multiply to N_0 to get 1. It's kinda like 1/0 but infinity. to 2nd comment: nah I'd rather do it anyway
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@ПавелПовх-з3у infinity is not on the number line. aleph null isn't either, but it can be shown on an extended number line
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@ПавелПовх-з3у so you can't "reach" N_0 just by adding 1 repeatedly.
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@fall4sleepfall4sleep26 yeah, that's what i thought, you didn't read the article! you just need to do 1 search on wikipedia to find the article about cardinals. it isn't that hard.
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@fall4sleepfall4sleep26 2 is a number. does that mean i need to tell you that 1+1=2 or give you any other "formular"? no! of course not! i don't need to give a formula for every little basic thing in math, so this just proves that you can't use basic thinking.
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@fall4sleepfall4sleep26 dude, you just ignored my proof that reals > naturals ok lets do this again first, i shall choose the 2 letters A and B to represent 0 and 1 next, i will make all strings with A and B and list then with your naturals. 1. 011010... 2. 011101... 3. 111011... 4. 111111... 5. 000000... ... next, i add a 0. at the start of all of those lists. 1. 0.011010... 2. 0.011101... 3. 0.111011... 4. 0.111111... 5. 0.000000... you remember binary? yes, what i have just written down is a list of all possible binary numbers between 0 and 1, and since binary is just a representation of numbers, this IS all the numbers between 0 and 1. refer to my proof from earlier if you want proof that size of numbers between 0 and 1 is greater than naturals.
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@fall4sleepfall4sleep26 game ended, just proved that all possible combos of 2 letters is bigger than the naturals.
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minor corrections to my proof: there should be a ... after the 5. part, "at the start of all of those lists" by lists i meant numbers
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@clurtzy uhm, haven't you considered the possibility that you don't understand? ok, i'll try my best to decipher your comment. infinite amount of names with no end? yeah, i get that. oh, so your point is all names are taken up? well, the way we make the new name is by making the 1st letter different from the first name's first letter, the 2nd is different from the 2nd of the 2nd name, and so on, so technically, by definition, you are wrong.
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@clurtzy *upon rereading, no, the point that all names are taken up is right, that's the definition of the set of names, what you aren't right about however, is claiming that the name we make is in the list already, which by definition, it isn't.
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@clurtzy also, please define "probably"? this is supposed to be about math, i am not suppose to deal with ambiguity here. anyways, i am positive that the new name is not on the list, not just "probably" positive.
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*reality.
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@fall4sleepfall4sleep26 any new games for me to play? it's been a while...
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@fall4sleepfall4sleep26 also, didn't the video literally prove that set of all letter combos size > naturals???? that was the point of the partybus part right?
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@robotnoir5299 um, yeah, most of the useful math is a reflection of reality, but some math can still be useful even if it cannot exist in reality like C^2 (4d complex space) as a simple example
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@robotnoir5299 not 100% of the useful part is in reality. i asked this earlier, but again, do numbers exist?
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@robotnoir5299 i didn't just name drop the rules of math earlier, i listed them and asked you which one do you have a problem with. (i know it's going to be axiom 7 because that specifically states that infinity exists but whatever) also, now that i think of it, positive numbers can be assigned to an amount of objects, so how about this instead: is -1 a "real"(exists irl) number?
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@pixelia6884 it's not a bigger infinity, both infinities are in fact size 2^aleph_0.
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@etmendz uh, all ab names are on the bus, the video ended with the fact that all ab named people on the bus can't possibly fit in the hotel, not that the bus isn't full.
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@Metal_Master_YT why the heck are limits even here in the first place? yes, i do agree that a "limit of 1" doesn't make sense. just because a completely irrelevant thing doesn't make sense, doesn't mean the whole concept is nonsense.
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@pixelia6884 ok np/yw i guess
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@robotnoir5299 also note: if youtube didn't want anyone to see your comment, why did it conveniently delete it AFTER i read it and AFTER i got to reply to it?
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@robotnoir5299 um, you cant prove that, and by occams razor or whatever, simplest explanation holds + to 2nd part, the youtube censor isnt intelligent, it does not care about if the comment was good or not, it just cares if it was inappropriate, which in this case, it isnt, because there are tons of r/badmathematics (yes i do use reddit) content on youtube that havent been deleted yet, so clearly, this filter that apparently deletes crank content doesnt seem to work
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@fall4sleepfall4sleep26 i never said that math is from nature either! read my comment again.
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@fall4sleepfall4sleep26 ok, so me being arrogant is relevant in what cardinals mean in freaking math?
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@ПавелПовх-з3у what the heck does reach it couple of times mean?
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@fall4sleepfall4sleep26 uh, the infinity of the rationals and the infinity of the naturals are the same. it would be a draw.
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@fall4sleepfall4sleep26 i won't outlast you, sure, but i can prove in a finite amount of time why my infinity is bigger or smaller than yours.
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@fall4sleepfall4sleep26 i choose the reals, and i will now prove why the reals are more numerous. lets first state that the size of the naturals is a cardinal number, called aleph 0, or N_0 for short. next, try to show a 1 to 1 correspondence with the naturals (N_0) and the reals between 0 and 1. 1. 0.92848287373727... 2. 0.838274991873848... 3. 0.848479292841910... 4. 0.928391938488288... 5. 0.828478283838828... ... I can order the reals between 0 and 1 any way i like, because there is no way to find the next number in the reals. next, take the first digit of the first number, which is in this case 9,and add 1 unless it's 9, which it is, so subtract 1, and make a new decimal starting with that number (0.8). next, get the 2nd of the 2nd number (3) and add 1 and put it in the new string of numbers. (0.83) repeat. (0.83948...). there we go, a new number that's guaranteed to be different to ALL the numbers on the list, because we defined it to be different. as you can see, I just proved that the numbers 0<number<1 is bigger than the naturals. next, lets prove all of the reals. first notice that the reals will be the exact same form as the numbers between 0 and 1, except you put a natural at the start. (after all, the numbers between 0 and 1 are all the decimals possible, all numbers of the form 0.something) since the size of the naturals is N_0 by definition, we can multiply N_0 and the size of the numbers between 0 and 1, and by the rules of cardinal math, big infinity will absorb small infinity, and since i just proved that (size of numbers between 0 and 1) > (size of your set, the naturals), i have just proven that the size of the set R, the reals, is bigger than the size of N, the naturals. any complaints?
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@fall4sleepfall4sleep26 i just gave you a proof, and i recommend you read it.
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@fall4sleepfall4sleep26 in math, you don't just do something like pick a number infinitely many times, you prove things, because picking a number is obviously impractical and as you said, proves nothing.
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@fall4sleepfall4sleep26 for example, is sqrt(2) a fraction? you can check all the decimal places, but that would take an infinite amount of time, and that's no good, so we resort to proving it instead.
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@fall4sleepfall4sleep26 Q.E.D. (note: i like how you say ":)" as if you have outsmarted me.)
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@fall4sleepfall4sleep26 i gave you a "formular", are you gonna understand it, is the question.
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@fall4sleepfall4sleep26 also I'm on a phone, not a browser.
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@fall4sleepfall4sleep26 i know you won't run out of numbers, and neither will i, but that doesn't mean i cant prove that you have less numbers than me.
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@clurtzy also it doesn't matter if you can't get to the end in real life, this is math, you can do anything in mathland. haven't you at least read my previous comments? i just realized the only reason i am arguing here is because people cannot accept that math is NOT based on realitym
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@fall4sleepfall4sleep26 oh yeah, forgot that people need sleep too im sorry
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@fall4sleepfall4sleep26 i wont have more? well i just undeniably proved it, tell me, what is wrong with the proof?
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@fall4sleepfall4sleep26 also it isnt infinity, cardinality and infinity behave differently, if it was infinity, then yeah, it wouldn't be bigger. unfortunately, it isn't infinity, so your argument falls flat.
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@cuongdarma1689 people don't learn this in school is probably the reason at least i never learned this in school
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@robotnoir5299 making up numbers that cannot exist is fine for comic books, yeah, i guess it is? also, infinity stones in the movies is just a name, it doesn't literally mean infinite stones
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@robotnoir5299 yes, it is absolutely dumb to argue who would win in reality, but again, this is math
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@robotnoir5299 also, when the hell did math need to prove that calculations reflect reality?
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@robotnoir5299 has there been a moment where it has been useful? yes! it's called the halting problem. it's actually more of an anti useful, since it proves that computers can't do everything, but idc i need to respond to the rest of your argument
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@robotnoir5299 the entire universe MAY conspire to never allow infinity to happen, but yknow, there is always a chance that we're wrong, and "tachyons" could potentially exist
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@robotnoir5299 crying dunning kruger? yeah, i seriously cannot think of any other arguments after repeating the same 2^N_0 is in fact greater than N_0 a good high amount of times
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@robotnoir5299 also, i am not trying to sell anything (did i take this too literally?), also also, i gave proof, also also also, upon rereading, the part about axioms isn't something i just typed out in hopes that will save me, it's something i typed out in response to the part where you asked about mathematicals rules
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@robotnoir5299 do you have a reliable source saying math is based on reality? i am actually quite interested in that, although that renders things like complex numbers, cardinals(obviously), P-ADIC numbers, numbers themselves (abstract concepts that don't exist irl)
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@robotnoir5299 yes, looking at the comic book would make me look stupid, but it's more like looking at the textbook and saying "1+1 = 2 because this thing says so!" of course, the textbook made up the rules of math as well, but unlike comic books, it sounds less ridiculous because textbooks rulez or whatever
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(by renders things like [useful math] i mean renders things like [useful math] nonexistent
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)
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@robotnoir5299 also, it isn't just MY imagination, it's MOST OF THE MATHEMATICAL COMMUNITY that decided that ZF good and cardinals real
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@Metal_Master_YT the list does not contain everyone on the bus because it is provable that you can make a new name not already on the list
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@Metal_Master_YT also, he should be in the bus, because the bus by definition has all people who have infinite strings of A and B in their names
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@richardhill9270 but the diagonal combo by definition was not on the list, since it is different from the first by the first letter, the second by the second letter, etc. his point was that a 1 to 1 function from N to all infinite combos of a and b does not exist because you can always definite another infinite string that isnt on the list
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@richardhill9270 "the diagonal concept isn't even true for a finite number" oranges are not yellow, therefore the closely related lemon can't be yellow either? "a whole number of other hurdles" wait, there are hurdles??? "be an infinite string of As" how? why can't you just change it to ABBAABABAAABA... or something? what's preventing that from happening?
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@richardhill9270 dude, we are talking about infinite decimals, you're comitting apples and oranges fallacy. just because something isn't true for finite decimals, doesn't mean it isn't true for infinite decimals.
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@richardhill9270 that's his stipulation? who's "his"?
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@richardhill9270 where in the definition of infinity says that you can't have a complete list????
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@richardhill9270 it isn't incomplete. you just can't understand the contradictory nature of 2^aleph_0.
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@robotnoir5299 also, why are you making arguments for everyone else? you're piggybacking off of the other person's argument to make some sort of ultimate comeback to finally once and for all 0wn me even though you literally just repeated points i already said false before? just because 4 other people say it's true, doesn't mean it is true. (note:the math community has more than 6 people. )
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@richardhill9270 you are missing something, you can't test it in the real world, but you can test it in math! ABABABAB... AABABABA... AABABABA... AAABAAAB... ... if you try to flip the letters, you will always have a letter to flip, because it's infinitely long. BAAAAAAA...
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@richardhill9270 also, defies the definition of what word exactly?
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@richardhill9270 when did complete require an end? the set of all numbers 1 2 3 4 5 ... has no end and isn't incomplete!
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@richardhill9270 it's weird how 1, 2, 3, ... is a counterexample to your claim that completeness is finite...
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@richardhill9270 we HAVE a reason to believe it works on an infinite set, he literally mentions it in the video! just because finite sets don't work doesn't mean infinite sets don't work. they're different.
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@richardhill9270 uhh, it wasn't a complete list, that's the whole point of the diagonal argument
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@richardhill9270 how is it completely different? spreadsheet is used to represent sets here in a hotel-manager-like way,and arrays are a programming thing, not a math thing.
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@richardhill9270 how could numbers touch? how do you make the finite contact with the infinite?
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@etmendz no it does not. the DEFINITION of the bus is that it contains all people that have names with a and b that are infinitely long. you cant argue with a definition. also, it does not have all the ab people in the world, it just has a bunch of people who's names have a and b, not EVERY person with names that only have a and b.
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@Metal_Master_YT i do know it's not on the list because by definition it isn't. same exact action x to make the new name? we only need to make 1 new name to prove that one infinity is smaller and the same action doesn't always lead to the same output (in 1+3 and 2+3, you're both adding 3, therefore 4=5?)
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@Metal_Master_YT why would the limit be one? why are limits related at all?
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@Metal_Master_YT there is no such thing as absolute infinity in most maths.
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@Metal_Master_YT how are higher dimensions involved? you could use a subset of the powerset of Z^2, but that adds unnecessary complexity to the problem.
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@Metal_Master_YT i'm sorry man, i can't exactly decipher this, it's very clear that this explanation is... not even wrong? idk, the base premises aren't even math statements, there isn't really anything worth noting here.... sorry if i misunderstood....
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