On 14/07/2013 08:51, Le_Forgeron wrote:
> Le 14/07/2013 00:28, Warp nous fit lire :
>> Orchid Win7 v1 <voi### [at] devnull> wrote:
>>> Consider for a moment the set of all natural numbers, N. This is (by
>>> definition) a countable set. Yet the set of all possible subsets of N is
>>> *uncountable*. And that's just plain ordinary subsets; the decimal
>>> expansion of a number is not merely a subset of N but an *ordered
>>> sequence* of digits. Intuitively it sounds like there should be *more*
>>> of these. (But, as with many things in set theory, it turns out actually
>>> the cardinalities are the same.)
>>
>>> Wikipedia explicitly mentions this:
>>
>>>
http://en.wikipedia.org/wiki/Cardinality_of_the_continuum#Alternative_explanation_for
>>
>> Perhaps the mapping you proposed between the points on a unit line and
>> the ones in a unit square is indeed valid.
>>
>> Although proving that it indeed is would be better than by something else
>> than "can you show me a counter-example?" :)
>>
> That's remind me of the old metaphor of the hotel of infinite rooms used
> for dealing with infinity.
>
> 1. the hotel is empty
> 2. a bus of infinite capacity (Aleph0 only, countable infinity) arrives.
> Each passager get the room number from its place in the bus.
> 3. a single guy came in. Current customers get moved from room N to room
> N+1. The guy get the first room.
> 4. another bus of same infinite capacity... Current customers get moved
> from room N to room 2N, passagers get the room 2s+1, where s is the seat
> number in the second bus.
>
> and so on.

What happens if an infinite number of buses turn up at once?

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