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wu :: forums    riddles    medium (Moderators: SMQ, Grimbal, Icarus, william wu, Eigenray, towr, ThudnBlunder)    Adding Cantor Sets « Previous topic | Next topic » Pages: 1  Notify of replies Send Topic Print    Author  Topic: Adding Cantor Sets  (Read 304 times) william wu wu::riddles Administrator     Gender: Posts: 1291 Adding Cantor Sets   « on: Sep 8th, 2003, 5:08am » Check out this nifty problem listed in the Putnam section, called Adding Cantor Sets. You're asked to prove a statement. The problem is in that section because a nonconstructive proof could potentially involve higher level math. However, you can try to find a constructive proof, which involves nothing but the ability to add.   http://www.ocf.berkeley.edu/~wwu/cgi-bin/yabb/YaBB.cgi?board=riddles_put nam;action=display;num=1063022553;start=0   Note: This thread is now locked (no one can post to it). To prevent duplicating information, please direct all posts regarding this problem (whether regarding the easy constructive proof, or harder nonconstructive proofs) to the putnam thread linked directly above. - WW « Last Edit: Sep 9th, 2003, 8:45am by william wu » IP Logged [ wu ] : http://wuriddles.com / http://forums.wuriddles.com Barukh Guest Re: Adding Cantor Sets   « Reply #1 on: Sep 8th, 2003, 10:27am » William, that's a very nice problem!   What if represent Cantor set elements as number in radix-3? IP Logged william wu wu::riddles Administrator     Gender: Posts: 1291 Re: Adding Cantor Sets   « Reply #2 on: Sep 8th, 2003, 1:23pm » Barukh: Yes I like it very much as well. In response to your hidden hint, that's a good way to start. Although you can make a nonconstructive proof that doesn't deal with that. IP Logged [ wu ] : http://wuriddles.com / http://forums.wuriddles.com Icarus wu::riddles Moderator Uberpuzzler Boldly going where even angels fear to tread.     Gender: Posts: 4863 Re: Adding Cantor Sets   « Reply #3 on: Sep 8th, 2003, 4:00pm » I see the method I mentioned in that thread is given in hint here. Still, it is a nice way of understanding what is in the Cantor set - besides leading to an easy way of calculating the Cantor-Lesbegue function. IP Logged "Pi goes on and on and on ... And e is just as cursed. I wonder: Which is larger When their digits are reversed? " - Anonymous Pages: 1  Notify of replies Send Topic Print Forum Jump: ----------------------------- riddles -----------------------------  - easy => medium   - hard   - what am i   - what happened   - microsoft   - cs   - putnam exam (pure math)   - suggestions, help, and FAQ   - general problem-solving / chatting / whatever ----------------------------- general -----------------------------  - guestbook   - truth   - complex analysis   - wanted   - psychology   - chinese « Previous topic | Next topic »

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