Reminder:
A countable set of countable sets is countable.
A countable set of countable sets is countable.
2007-04-27
Rachel
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'You gave me hyacinths first a year ago;
'They called me the hyacinth girl.'
Yet when we came back, late, from the Hyacinth garden,
Your arms full, and your hair wet, I could not
Speak, and my eyes failed, I was neither
Living nor dead, and I knew nothing,
Looking into the heart of light, the silence.
Od' und leer das Meer.
-- T.S. Eliot
2 Comments:
Yes! This is Cantor's Theorem, which was presented to me by my Intermediate Analysis prof as a part of Quark's Dilemma.
Quark has a hotel with an infinite number of rooms, and during a starfleet convention an infinite number of borg ships show up each bearing an infinite number of borg. But Jean-Luc Picard and the Federation have occupied all the rooms already. So what's a poor Quark to do?
Tell everyone in the hotel to move to the room number twice that of the room they are currently in. Suddenly an infinite number of rooms are available, but there are infinitely many ships full of infinitely many borg! So what's a poor Quark to do?
Start taking on paying clients in the following order -
(1) (2) (6) (7) ...
(3) (5) (8) ...
(4) (9) ...
(10) ...
...
and so on where the column # is the ship and the row # is the passenger. Thus assuring all the borg passengers a place, Quark's coffers are lined with latinum.
Adorable. I was applying it to my to-do list, but I like this better.
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