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Subject: Tristam Understood Author: Duane [ Next Thread | Previous Thread | Next Message | Previous Message ] Date Posted: 09/ 9/04 1:48am In reply to: Duane 's message, "Finally.... Tristam meets his doom.... (bleah)" on 08/31/04 5:56am Wade: OK. I finally understand. Here's the nature of the paradox: These are statements provable in Cantor set theory - 1) Two sets have the same cardinality (i.e., the same number of elements) if there exists a total, one-to-one and onto function mapping one set to the other. 2) A set is countably infinite if it has the same cardinality of the natural numbers. Now, according to the Tristam "paradox," the following situation exists: The set of days is countably infinite The set of years is countably infinite Therefore, the set of days is the same size (that size being "countably infinite") as the set of years. These things are true. And they are weird. But the simple fact remains that they don't "prove" anything. The declaration of "absurdity" does not equal disproof. So I fail to see how the Tristam Shandy "paradox" says anything substantiative. Duane [ Next Thread | Previous Thread | Next Message | Previous Message ]

Replies:

Subject Author Date I think Damoclese 09/10/04 10:22am Yes - I agree -- Duane, 09/11/04 2:27am Nods head -- Damoclese, 09/11/04 10:45pm In fact.... -- Duane, 09/11/04 2:42am Well days and years are nothing but ... Don 09/11/04 2:14pm Long time, no see. -- Damoclese, 09/11/04 11:47pm yep - profundities abound... -- Duane, 09/12/04 4:44am and sometimes with profundities come headaches -- Damoclese, 09/13/04 1:53am Chat Thingy -- Duane, 09/13/04 6:21am Sounds good -- Damoclese, 09/13/04 5:21pm You wrote a very interesting post Duane -- Don, 09/16/04 1:06pm Thanks! -- Duane, 09/17/04 5:55am I never fought with that question of -- Don, 09/16/04 12:05pm Simple answers aren't always good answers -- Damoclese, 09/16/04 2:53pm Did you? Wade A. Tisthammer 09/12/04 6:19pm Yes, but I'm beginning to think that maybe you don't... -- Duane, 09/13/04 8:21am I understand my own argument, you evidently do not. -- Wade A. Tisthammer, 09/13/04 11:46pm Ah - apparently we're talking about 2 different things. -- Duane, 09/14/04 4:37pm Perhaps. -- Wade A. Tisthammer, 09/26/04 9:32pm And just for fun... -- Duane, 09/13/04 8:38am Just for fun, let's deal with the actual premises -- Wade A. Tisthammer, 09/13/04 11:55pm You have no idea Wade..None... -- Don, 09/16/04 8:15pm Yes I do. You evidently do not. -- Wade A. Tisthammer, 09/26/04 9:39pm Making sure we understand each other -- Duane, 09/17/04 4:01am Groovy. -- Wade A. Tisthammer, 09/26/04 9:54pm