TED: The Infinite Hotel Paradox

Submitted by: richanddead 3 years ago in Science

The Infinite Hotel, a thought experiment created by German mathematician David Hilbert, is a hotel with infinite rooms.
There are 20 comments:
Male 8,543
Nice pic, richanddead, but that`s an illustration of Zeno`s "Achilles and the tortoise". A type of Dichotomy paradox, but not the same.

In Zeno`s "Dichotomy paradox", Homer is attempting to reach a fixed spot (a stationary bus), he never reaches it because me must first complete an ever smaller half-distance unto infinity.

In Zeno`s "Achilles and the tortoise", Achilles is attempting to a catch a moving (albeit slow) target..the tortoise. Achilles will never catch the tortoise as whenever he reaches where the tortoise was, the tortoise has moved on. The distance between the two become infinitely small, but do not reach zero.

I saw paper presented on this years ago. Thought it was interesting paradox, but fails in the real world.
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Male 8,543
DromEd-"[quote]Why can`t he just hand the next guest the next key instead of pissing off an infinite number of people buy asking them to move?[/quote].

Because there aren`t currently any empty rooms. He only creates empty rooms when someone moves.
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Male 2,694
Why can`t he just hand the next guest the next key instead of pissing off an infinite number of people buy asking them to move?
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Male 40,752
@Jake_Justice: You bet they`re clean! Didn`t you see that hard working maid? ;-)

I :heart: Zeno! His Arrow Paradox still rules!
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Male 40,752
1:23 "Countably Infinite"?
Isn`t that an oxymoron? :-/

You`d need an infinite amount of time to pass out all those keys...

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Male 1,627
""But I have to wonder: What is the point?"
That a mathematician that specializes in thought experiments would be a lousy hotel manager since he`d keep asking people to move around for no reason, causing an infinite number of people to leave without paying... "


when I learned this it was an example to teach induction. all induction is, is that, if you can prove that an `n` exists, you can prove an `n+1` exists too. its hard to grasp at first but it`s cake. also n has to be a number. you cant prove infinity and than infinity +1
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Male 1,627
welcome to discrete math 101.
also he pronounced aleph null wrong, or at least different than I`ve ever heard a professor say it.
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Male 4,099
Zeno`s Dichotomy paradox


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Male 8,543
[quote]Which means since it never ends you can never get to let alone pass 1 second.[/quote]

Not quite, as what you`re describing is just an infinite number of increments in which to measure that second. It does not mean you cannot pass that second.

Sounds alot like Zeno`s [quote]Dichotomy paradox[/quote] which states that when Homer tries to catch a stationary bus, he`ll never reach it because before he reaches it, he must get halfway there. Before he can get halfway there, he must get a quarter of the way there. Before traveling a quarter, he must travel one-eighth; before an eighth, one-sixteenth; and so on.

Ergo, he must complete and infinite number of tasks, which, in theory, is impossble.
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Male 7,031

This fails to take into account whether or not the infinite number of toilets in the infinite number of rooms have been sanitized for the protection of the infinite number of guests.

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Female 655
Lost me right around 2:55 lol
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Male 66
DuckBoy87, this is one of my favorites just for the fun of messing with people (the 0 to 1 thing). If infinity exists then there is no such thing as time. If 1 second exists, then half a second exists...and a quarter second... into an infinity of fractions. Which means since it never ends you can never get to let alone pass 1 second.
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Male 125
Draculya

"The solution is to multiply eternal judgement by the infinitesimally small likelihood of the existence of any god. Zero multiplied by infinity is zero. "


But infinitesimally small is not zero. Or have I misunderstood?
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Male 15,264
Welcome to the power of infinity. This is where logic breaks down.

That is why religions use the concept of notional eternal unimaginable reward and eternal unimaginable punishment to justify ridiculous and counter-intuitive, not to mention potentially immoral, acts of limited though heinous impact in the real world.

The solution is to multiply eternal judgement by the infinitesimally small likelihood of the existence of any god. Zero multiplied by infinity is zero.

Another solution is to deduct the teachings that conflict with one or more competing religions which may differ in outlook, as infinity minus one or multiple infinities is zero.

We must also acknowledge real world ethics/morality multiplied by the near perfect probability that the real world exists.

Therefore, religion ranks zero against true impact in order of priority.
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Male 5,626
"But I have to wonder: What is the point?"
That a mathematician that specializes in thought experiments would be a lousy hotel manager since he`d keep asking people to move around for no reason, causing an infinite number of people to leave without paying...
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Male 2,106
I still hate TED talks.
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Male 1,397
....this was infinitely specious IMHO.
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Male 3,646
I like these.

My two favorite infinity problems are:
1+2+3+4+5+6+ ... = -1/12
and
the number of numbers between 0 and 1 is greater than the number of counting numbers.
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Male 125
That was some nice animation explaining higher mathematics. But I have to wonder: What is the point?
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Male 4,099
Link: TED: The Infinite Hotel Paradox [Rate Link] - The Infinite Hotel, a thought experiment created by German mathematician David Hilbert, is a hotel with infinite rooms.
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