Chit Chat
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18 Nov 19
23:59
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21 May 10
If you were to walk from point A starting with a stride of four feet with each incremental step being half the length of the previous one, it would take an infinite number of steps to reach point B 12 feet away.
But what if you checked in to a hotel with an infinite number of rooms which were all occupied? Could you be accommodated?
But what if you checked in to a hotel with an infinite number of rooms which were all occupied? Could you be accommodated?
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off course
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Ja.
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No , the clue is in the word 'all'
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42
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The number of rooms in the hotel is actually infinity plus one.
This additional room can always be made available to accommodate surplus guests. |
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As long as every guest was prepared to move into the room next door, the first one would become vacant for you.
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That was what was said in the programme I watched, SFBTW.
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Hilbert's paradox of the Grand Hotel (colloquial: Infinite Hotel Paradox or Hilbert's Hotel) is a thought experiment which illustrates a counterintuitive property of infinite sets.
It is demonstrated that a fully occupied hotel with infinitely many rooms may still accommodate additional guests, even infinitely many of them, and this process may be repeated infinitely often. The idea was introduced by David Hilbert in a 1924 lecture "Über das Unendliche", reprinted in (Hilbert 2013, p.730), and was popularized through George Gamow's 1947 book One Two Three... Infinity. |
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Tripe , if all the rooms are occupied then that’s that
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LFC - It's a tough one to get your head round, which is why I asked the question but I'm not going to argue with esteemed mathematicians.
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nick , next these ‘ experts ‘ will be telling you you can stand and sit at the same time
That’s tripe also |
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Let me explain . If a hotel has an infinite number of rooms and they are not all occupied then you can find a room
If they are all occupied then you can’t I can’t say it any simpler than that |
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When you move the first guest to the next room, you have already made space for the guest you needed to accommodate. That all rooms are occupied doesn't matter because each guest keeps moving to the next room. They keep moving forever because there are infinite rooms. And they are all occupied. So there's always someone who can move.
The implication of all rooms being occupied is not that there's no free room. The implication is that every single guest is able to move to the next room. |
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MATH
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Ah , that’s a hotel with a potential infinite number of rooms
Not a hotel with an infinite no of rooms Of course if a hotel has 100 rooms , and 100 guests and then builds another room there will be room for another guest So what ? |
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POTENTIAL
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If you go to a hotel with an infinite number of rooms and they tell you they are fully booked then it's probably best to take the hint
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precisely so happy:]
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It’s like this , Yuu may want to walk 100 yds ,
So you walk 10 yds and then half of 10 and then half of ten etc etc ( in theory into infinity ) But I assure you no matter what you will come to the end of that 100 yds ( all being well ) |
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You see there is a fundamental flaw in MATHS
And indeed in probability No one really believes that if you toss a coin 99 times and each time it is tails that the chances of it being tails again next are 50 50 That’s what the maths says of course , no one believes that Because it’s not true. There is a fundamental flaw in maths |
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Please enlighten us.
What is the probability of tail on the first toss of the coin? And what is the probability of tails on the 100th toss given 99 previous tosses resulted in tails. |
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You need to remember that lfc1971 is a subject matter expert on probability, he holds the world record for backing the highest number of consecutive losers
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The only way that there may not be a flaw in maths is dependant on time ...and time must be infinite ( otherwise there is a fundamental flaw )
Of course time might be infinite , but that doesn’t help us in any practical way , because we are here now At this moment in time |
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Probably because he thinks the chances of his next bet being a loser again is now lower.
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LFC, with respect, I think you've got this wrong.
Look at it like this... If you back a 1/4 shot that's an 80% chance. If it wins, you roll up your stake and place it on another 1/4 shot and repeat. If you carry on, sooner or later you'll lose. The odds of winning 20 successive bets are about 127,000-1 but if you had 19 winning bets, the odds of the 20th bet winning is still 1/4. For you, it would be your 20th bet in a sequence but someone else will be placing the same bet as a one-off totally unaware of your winning sequence. |
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TIME
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Yes I know that’s the maths nick , it’s wrong
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Why is it wrong ? Because it depends on an infinite amount of time
We are only here for three score years and ten , there was no time for you , or I , or anyone else Before that , or after that |
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When you put it like that it makes sense.
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Let's say you back Liverpool to beat Brighton at 1/5. What if someone else is placing the same bet which is the 5th or 10th or 20th in a winning sequence of 1/5 shots?
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We were always told independent events do not influence each other's probabilities. Clearly a wrong concept.
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Look at it this way , if time comes to an end tomorrow
Then all that maths is WRONG |
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You can place 20 such bets bets within 10 hours, 10 days or 10 months.
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Cooperman , picture please .
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I’m not sure if anyone else has thought of that before
That might be worthy of a Nobel prize in science or maths ? Hopefully some of the scientific community are looking into chit chat |
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You don't intend to pursue this concept yourself?
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I am pretty sure if you were presenting this to the top 50 mathematicians in the world and refused to answer any of their questions like you do here, you will come out successful.
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If you're a bookmaker and someone wants £1k on a 1/5 shot and someone else wants £1k on the same bet but is on winning sequence of 10 bets, based on your theory, you'd be more likely to accept the latter.
But there is no difference. In fact, you probably would have no knowledge of his previous bets. |