andrewducker (
andrewducker) wrote2012-07-17 12:00 pm
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Interesting Links for 17-07-2012
- How Emma Sky went from anti-war academic to governor of one of Iraq's most volatile regions
- Screen Display Calculator - how far away should your TV be? And what size?
- Eight radical solutions to the childcare issue
- What did the Persians think of Alexander the Great?
- Free access to British scientific research within two years
- 7 reasons why I’m against DevoPlus / DevoMax
- Merely visiting a newspaper website can be a breach of copyright.
- How many infinities are there?
- The three options the Church Of England faces over same-sex marriage (well worth reading)
- Fifty Shades of Babe: Duke Nukem Reads E. L. James
- Facebook Engineer Responds to Imgur Block with Epic Reddit Apology
- US Security Agents At Heathrow For Olympics
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The rationals are easy to label: have a table with the integers on top and side, generating rationals by top/side (and being sensible about 0), then move diagonally back and forth labelling all the numbers. There will be some overlap, but it's fine to give the same number two labels when it can be presented in two different ways. There are, however, only countably many rationals between any two numbers, not uncountably many.
The take home message remains that there are two types of infinity that should suit most people.
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:-)
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Geeks FTW.
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(This glosses over some technical details about numbers with two binary representations but that doesn't make much difference)
Incidentally, Greg Egan once wrote a short story where it was critical to the plot that the Cantor set was uncountable. I'm pretty sure he did it to prove he could.
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When it comes down to it the properties of the Cantor set are quite remarkable... measure zero, nowhere dense, a complete metric space yet uncountable. No wonder it gave mathematicians of the age fits!
I mentioned elsewhere (not sure if in reply to you) Rudy Rucker's book "White Light" which also hinges on the countable, uncountable and other possible forms of infinity.