
A computational perspective on set theory - jlhamilton
http://terrytao.wordpress.com/2010/03/19/a-computational-perspective-on-set-theory/
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ihodes
What a fascinating article - rarely do you run across such well written math
material! I've got to disagree on the intuitiveness of Cantor's diagonal
theory, though; that was one of the most beautiful and intuitive proofs in set
theory for me: make a list (denumerable) of decimally expanded reals; change
the digit on the diagonal of each; you've now created a number not on the
list: QED. Bam.

~~~
ihodes
Really curious about the downvote—did I do something gouche?

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nsrivast
Is there a way to view vote history, or are people actually watching the
number of votes their comments get?

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buro9
The down vote isn't visible now, if that's what you're wondering.

I came into the thread just after it had started and the only comment was
ihodes. I thought it was interesting in that after reading the article I
shared some of the same thoughts but at this point that single comment was
down voted and with zero as the score.

I up voted it back to one and ihodes had already replied asking why it was
down voted.

So there's no visible history and he's not seeing down votes, just the final
score. It's just that the first vote was a down and he responded to that.

He has a fair question though on down vote policy. It's very hard to see why
it should've been down voted.

My policy is to up vote everything worthy of up voting but to only ever down
vote the really irrelevant, off topic and rude posts. Others do seem to down
vote really random things.

Maybe people should be asked for a reason when they down vote so that they
stop and think about it for a moment.

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cousin_it
Too bad the article didn't go all the way into computation-land, so I can't
readily believe the "finitariness" of the insights contained there. For
example, is the function E() actually implementable in Haskell? If it isn't,
the whole premise kind of collapses... One way to make sense of this question
would be to skip the red herring of constructibility and define reals as lazy
streams of bits, then try to write actual code and stuff. (But how in the
flying hell do you implement a rationality predicate on reals-as-streams?)
There are probably other, non-equivalent ways. This stuff isn't trivial at
all.

For a more enlightening perspective on such topics, see the blog "Mathematics
and Computation", especially those articles:

[http://math.andrej.com/2007/09/28/seemingly-impossible-
funct...](http://math.andrej.com/2007/09/28/seemingly-impossible-functional-
programs/)

[http://math.andrej.com/2008/02/06/representations-of-
uncompu...](http://math.andrej.com/2008/02/06/representations-of-uncomputable-
and-uncountable-sets/)

