Wikipedia:Reference desk/Archives/Mathematics/2007 November 11

= November 11 =

Is it a paradox?
I made a to-do list which consists of Does this require any more work, or I am done? (Igny 00:48, 11 November 2007 (UTC))
 * Make a to-do list
 * I'd say you are done. You want a to-do list, and you have one. -- Meni Rosenfeld (talk) 00:55, 11 November 2007 (UTC)
 * No paradox here. Just a self-reference. &mdash; Kieff | Talk 02:39, 11 November 2007 (UTC)
 * But a self-rerefence can create a paradox.(Igny 04:22, 11 November 2007 (UTC))
 * Suppose you go to the store and buy groceries. A week later, you run out. You write a to-do list that includes buy groceries. Are you done with that part?
 * Generally, a to-do list is telling you what to do after you make the list, so you'd need to make another to-do list. — Daniel 03:11, 11 November 2007 (UTC)
 * Items placed on a to-do list are, by nature, a description of tasks to be done in the future. If there is nothing else "to-do," yet making a to-do list remains of paramount importance, then you will be writing that short one-item list for a very long time indeed.  Sappysap 04:44, 11 November 2007 (UTC)


 * Oh - no - you're not done. Look at your to-do list...it says you've got to make another to-do list.  So make another to-do list, then cross the single entry off of the first list.  Now you have two to-do lists and they are BOTH empty - so NOW you're done. SteveBaker 05:47, 11 November 2007 (UTC)


 * It says only to "make a to-do list." It doesn't say what is to be on that list. It doesn't necessarily have to say "make a to-do list." It could say "stop making to-do lists." ... But what if the second list says "ignore first to-do list"? — Michael J  07:58, 11 November 2007 (UTC)

Your thinking however is close related to a paradox in naive set theory which lead to the now common ZFC axiomization of set theory. (I think it was called Russell's paradox but I'm not sure.) A math-wiki 10:50, 11 November 2007 (UTC)
 * I started out in the direction of "Does the to-do list that lists all todo-lists that list a to-do list, contain itself?", but it's not a paradox, since it's not self-reference. Just recursion. Of course, when you're making a to-do list, you can start with "Make this to do list" (to be crossed off when you've finished writing the list). Then you can imagine the to-do list that tells you to make all such to do lists (ie., the set of all sets that contain themselves). Then there's also the to-do list that tells you to make all to-do lists that that do not contain "make this to-do list". Does that list tell you to make itself? That is, I think, roughly equivalent to Russel's paradox. risk 19:00, 11 November 2007 (UTC)


 * I'm not sure where, but I heard of a guy who had his book translated into French by a friend, and added at the end (in French), "I would like to thank my friend for helping me translate the preceding book. I would like to thank my friend for helping me translate the preceding sentence. I would like to thank my friend for helping me translate the preceding sentence." Why did he stop after two? Black Carrot 21:25, 15 November 2007 (UTC)


 * Humorous effect I believe :) A math-wiki (talk) 10:17, 17 November 2007 (UTC)