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.

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