Berkeley CSUA MOTD:2010:June:29 Tuesday <Wednesday>
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 2010/6/29-7/2 [Uncategorized] UID:53869 Activity:kinda low ```6/25 Does anyone actually have a direct proof as to why the Irrational Numbers are countable, (one that doesn't start with "assume they are countable.." Thx. \_ No, it's not possible. "Uncountable" means "can't be put into one-to-one correspondence with the natural numbers"; the only way to prove an impossibility like that is to assume the opposite and derive a contradiction. Mathematicians who reject the idea of proof by contradiction also reject the idea of uncountable sets. See http://en.wikipedia.org/wiki/Constructivism_(mathematics \_ Interesting- i are these folk discredited? I ask because there are an awful lot of proofs (including the halting problem, not the version that is directly from cantor's diagonal tho) that always start out with "assume this is true..." \_ I really don't think you'll find a proof that irrational numbers are countable. \_ they're not countable.```
 2010/6/29-7/20 [Reference/BayArea] UID:53870 Activity:nil ```6/25 I'm a newbie trying to learn SF neighborhoods, which seem to be a colloqial concept not written down anywhere. Is there a map like the following (but higher res) that looks like this? http://en.wikipedia.org/wiki/File:SF_Noe_Valley.png \_ http://lmgtfy.com/?q=%22san+francisco+neighborhoods%22 \_ http://www.sfarmls.com/docs/areamaps.htm the only non pretensious map. \_ And hence totally useless for learning the traditional names \_ would it be pretentious to point out your spelling error? \_ enjoy http://en.wikipedia.org/wiki/Neighborhoods_in_San_Francisco```
Berkeley CSUA MOTD:2010:June:29 Tuesday <Wednesday>