What most people fail to realize is that infinite sets are NOT ALL EQUAL. Take, for example, all the numbers in-between 0 and 1. this is an infinite series that is smaller than the numbers between 0 and 2. Originally the hotel had two equal infinite sets: guests and rooms. The initial statement of "No Vacancies" indicates that the room and guest sets (although infinite) are fixed. The reason the idea of the hotel works is because the hotel is cheating by expanding its room set.
you cannot increase the size of infinity without being its equal. we knows that is not possible. but an infinity can absorb the number 1. my precious solution.
Yeah, but what's the purpose of adding infinity to infinity, it's still infinity, nothing changes. This adventure in thought is stupid because infinity is not possible, let alone, having infinity x2, so it's rather pointless.
@Swolf943 Not exactly pointless. It should be said that finite mathematics is possible and probably cultivated by a few mathematicians, but it is much less useful than mathematics with infinities. Ask any physicist. The universe they propose is finite, yet infinities turn out to be indispensable in the explanation of it.
You forgot the third part : If an infinite amount of people came on a infinite amount of buses each one containing an infinite amount of people. Possible if there is an infinite amount of prime numbers which there is
better yet, the whole idea is fake. as if the where infinite rooms and guest, there wouldnt be anything new.. since there is no end the is no beggining..
...continued If it had all fractions as a room, then doubling each person's room number wouldn't matter, because every room has a room half of itself. When you are limited to integers (no fractions) odd numbers cannot be divided by 2 into another integer, thus providing the "illusion" of empty space. When in fact, if the hotel REALLY had infinity rooms, even odd numbered rooms would be filled when fractions are doubled.
This is why it seems wrong. This hotel has an infinite amount of rooms, but not infinity rooms. Let me explain: It has all positive INTEGERS of rooms, which is an infinite amount of rooms, but not infinity rooms. If I would say "How many room does it have between 3 and 5" you see that part of the hotel has finite rooms. A TRULY infinite hotel would have a room for every single fraction. Then there are infinite rooms between 3 and 5. (just example numbers). continues...
@oriocoookie No. That isn't true. No set can be a proper subset of itself. However, infinite sets do have proper subsets which are equinumerous to them.
@oriocoookie No, that is not the definition. The definition of a Dedekind-infinite set is that it has a proper subset of the same cardinality. The notion of a set which its own proper subset is absurd. If A is a proper subset of B, then in particular A is not equal B. If A were a proper subset of A, then A would have to be different from A, which would violate the axiom of extensionality.
@IsraeliXdude Well, it's not a paradox proper, it's a detail of counting infinite sets, like, for instance, the set of all positive whole numbers, N.
The catch with the hotel is that, if you were to count all numbers in N, then all the even positive ints, and all odd positive ints, you'll reach the same number (because you can match each 2n with an n, and each 2n+1 with an n, ad infinitum)... despite the two sets being a partition of N. Basically, infinity + infinity = the original infinity.
@StrikaAmaru Is infinity odd or even? positive or negative? infinity is not an integer, the moment you sum infinity it becomes integral, how integral can be infinite?
@IsraeliXdude "odd or even" - not defined. "positive or negative" - both, but with different infinities. ANd I really can't figure out what you said in the rest of the comment, or how it ties in with my comment :/
@StrikaAmaru People tend to perceive infinity as a number which is not true, Infinity+1=? Infinity-1=?
It doesn't if you to ask person move to n2 of his room number or 10n, if each person to move 10n then 1-10 2-20 3-30.... all integrals which are divided by 10 with fraction of as a result will be available, what im trying to say is that you cannot apply any arithmetics to infinity.
@signedadam It's not that it's not real, it's just people getting stupid playing with numbers. Look at the Hotel as you may look at the planet, people are coming and going all the time. Hilberts theory doesn't take into account people dying off, this happens all the time. I think there might be use for this in population science, if people take more things into account.
I'm an idiot...can someone describe this to me in layman's terms? I do not fully understand it...
MrTryfe 1 day ago
What most people fail to realize is that infinite sets are NOT ALL EQUAL. Take, for example, all the numbers in-between 0 and 1. this is an infinite series that is smaller than the numbers between 0 and 2. Originally the hotel had two equal infinite sets: guests and rooms. The initial statement of "No Vacancies" indicates that the room and guest sets (although infinite) are fixed. The reason the idea of the hotel works is because the hotel is cheating by expanding its room set.
TheEmperorGulcasa 4 days ago
Apparently... infinity have different values.
Athrun000 1 week ago in playlist 60 Second Adventures in Thought
you cannot increase the size of infinity without being its equal. we knows that is not possible. but an infinity can absorb the number 1. my precious solution.
MrSharewndws 4 weeks ago
you don't add to infinity. infinity adds to you.
MrSharewndws 4 weeks ago
whats the point of this one?
sniped101 1 month ago
I love your Channel!
MiriamLeis 1 month ago
Infinity doesn't even exist, adding infinity to infinity isn't even possible since infinity is already infinite.
Swolf943 2 months ago
@Swolf943 thats why it equals infinity because infinity is not a finite number
DheRadman 2 months ago
@DheRadman
Yeah, but what's the purpose of adding infinity to infinity, it's still infinity, nothing changes. This adventure in thought is stupid because infinity is not possible, let alone, having infinity x2, so it's rather pointless.
Swolf943 2 months ago
@Swolf943 Not exactly pointless. It should be said that finite mathematics is possible and probably cultivated by a few mathematicians, but it is much less useful than mathematics with infinities. Ask any physicist. The universe they propose is finite, yet infinities turn out to be indispensable in the explanation of it.
mmasny 1 month ago
You forgot the third part : If an infinite amount of people came on a infinite amount of buses each one containing an infinite amount of people. Possible if there is an infinite amount of prime numbers which there is
insaneguitarfrettet 2 months ago in playlist Liked videos
for this to work the hotel would have already needed an infinite amount of rooms, so the guest shouldn't have had to move into another room, anyhow
mgs4227 2 months ago
i love this series and its humour hahaha! and the narator really sounds like david mitchell!
jaymayhoi 2 months ago in playlist More videos from OUlearn
better yet, the whole idea is fake. as if the where infinite rooms and guest, there wouldnt be anything new.. since there is no end the is no beggining..
truthismygod 2 months ago in playlist Más vídeos de OUlearn
Actually the paradox is that infinite as a concept/numerical value/anything is paradoxical in nature
Wutwut1n1 2 months ago
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imagine 2 infinite lines of numbers.
Imagine one line with all the numbers 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, ect
The other would contain the numbers 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24..ect
Now both lines are infinite, so both lines have the same infinite amount of numbers. right?
How can line 1 and line 2 have the same amount of numbers when in line 2 we know you only have half? Infinity sucks !
timen1986 3 months ago in playlist 60 Second Adventures in Thought
...continued If it had all fractions as a room, then doubling each person's room number wouldn't matter, because every room has a room half of itself. When you are limited to integers (no fractions) odd numbers cannot be divided by 2 into another integer, thus providing the "illusion" of empty space. When in fact, if the hotel REALLY had infinity rooms, even odd numbered rooms would be filled when fractions are doubled.
danielcarmi305 3 months ago in playlist 60 Second Adventures in Thought
This is why it seems wrong. This hotel has an infinite amount of rooms, but not infinity rooms. Let me explain: It has all positive INTEGERS of rooms, which is an infinite amount of rooms, but not infinity rooms. If I would say "How many room does it have between 3 and 5" you see that part of the hotel has finite rooms. A TRULY infinite hotel would have a room for every single fraction. Then there are infinite rooms between 3 and 5. (just example numbers). continues...
danielcarmi305 3 months ago in playlist 60 Second Adventures in Thought
What if infinitely many buses arrive at the hotel each carrying an infinite number of passengers?
HallmarkJD 3 months ago 2
@HallmarkJD Then you're screwed.
truezenwarrior15 3 months ago
This is gypsy witchcraft
xDoctorMooch 3 months ago
why doesnt the new guest just go to a vacant room?
patrimacc 3 months ago
too bad infinity is not a number, it's merely a simple for there's no largest number
ZhangyXD 4 months ago
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Neat art
mattysimsoficial 5 months ago
Nlhahaha neat art.
mattysimsoficial 5 months ago
the paradox is that infinite sets are proper subsets of themselves
oriocoookie 5 months ago in playlist 60 Second Adventures in Thought 26
@oriocoookie No. That isn't true. No set can be a proper subset of itself. However, infinite sets do have proper subsets which are equinumerous to them.
mmasny 1 month ago
@mmasny i thought that that was the definition of an infinite set ... it is a proper subset of itself .... check cantor
oriocoookie 1 month ago
@oriocoookie No, that is not the definition. The definition of a Dedekind-infinite set is that it has a proper subset of the same cardinality. The notion of a set which its own proper subset is absurd. If A is a proper subset of B, then in particular A is not equal B. If A were a proper subset of A, then A would have to be different from A, which would violate the axiom of extensionality.
mmasny 1 month ago
Where is the paradox? room will be free the period of time the guest will spent moving from one room to another
IsraeliXdude 5 months ago 2
@IsraeliXdude Well, it's not a paradox proper, it's a detail of counting infinite sets, like, for instance, the set of all positive whole numbers, N.
The catch with the hotel is that, if you were to count all numbers in N, then all the even positive ints, and all odd positive ints, you'll reach the same number (because you can match each 2n with an n, and each 2n+1 with an n, ad infinitum)... despite the two sets being a partition of N. Basically, infinity + infinity = the original infinity.
StrikaAmaru 4 months ago 8
@StrikaAmaru Is infinity odd or even? positive or negative? infinity is not an integer, the moment you sum infinity it becomes integral, how integral can be infinite?
IsraeliXdude 4 months ago 2
@IsraeliXdude "odd or even" - not defined. "positive or negative" - both, but with different infinities. ANd I really can't figure out what you said in the rest of the comment, or how it ties in with my comment :/
StrikaAmaru 4 months ago
@StrikaAmaru People tend to perceive infinity as a number which is not true, Infinity+1=? Infinity-1=?
It doesn't if you to ask person move to n2 of his room number or 10n, if each person to move 10n then 1-10 2-20 3-30.... all integrals which are divided by 10 with fraction of as a result will be available, what im trying to say is that you cannot apply any arithmetics to infinity.
IsraeliXdude 4 months ago
@IsraeliXdude ROFL
daviangel 3 months ago
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lol, that can't be real
signedadam 5 months ago
@signedadam It's not that it's not real, it's just people getting stupid playing with numbers. Look at the Hotel as you may look at the planet, people are coming and going all the time. Hilberts theory doesn't take into account people dying off, this happens all the time. I think there might be use for this in population science, if people take more things into account.
SiriusMysterious23 3 months ago