Timeline for Proving the existence of disjoint subsets
Current License: CC BY-SA 3.0
13 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jan 18, 2015 at 18:25 | vote | accept | CommunityBot | ||
| Jan 18, 2015 at 4:53 | review | Suggested edits | |||
| Jan 18, 2015 at 5:11 | |||||
| Jan 18, 2015 at 4:51 | answer | added | Tad | timeline score: 3 | |
| Jan 18, 2015 at 1:54 | comment | added | user198185 | Ah I see, using the Power set. Now I see how to use the Pidgeonhle Principle. Thank you! | |
| Jan 18, 2015 at 0:22 | comment | added | Tad | You have to be a little more careful than this. While there are $2^{n+1}$ choices for $I$ and only $2^n$ choices for the union, that only tells you there must be lots of pairs $I$ and $J$ which give the same union -- but it doesn't guarantee that $I$ and $J$ will be disjoint. | |
| Jan 17, 2015 at 23:07 | comment | added | user198185 | So would the number of choices for I, J be $n!$? Unsure of the number of options for the union, would it be $n!$ as well? | |
| Jan 17, 2015 at 22:46 | history | edited | user198185 | CC BY-SA 3.0 | I noticed the question has been re-tagged as "combinatorics", but it should be noted I have never taken a course in combinatorics (this question is from an algebra course) and so I have no familiarity with many of its concepts. |
| Jan 17, 2015 at 22:00 | comment | added | Fiktor | Count amount of choices for $I$ and amount of options for $\bigcup_{i\in I} A_i$. | |
| Jan 17, 2015 at 22:00 | comment | added | user207868 | Oh, I see: it is time to go to bed. A hint for the OP: use the pigeonhole principle. | |
| Jan 17, 2015 at 21:58 | comment | added | Tad | @LeonAragones: your set $A$ does not have $n=2$ elements. | |
| Jan 17, 2015 at 21:56 | comment | added | user207868 | I'm not sure if it is true. Let's set $n = 2$, $A = \{1, 2, 3\}$ and $A_k = \{k\}$ for $k \in \{1,2,3\}$. Can you find disjoint and nonempty $I$ and $J$? | |
| Jan 17, 2015 at 21:50 | history | edited | Asaf Karagila♦ | edited tags | |
| Jan 17, 2015 at 21:28 | history | asked | user198185 | CC BY-SA 3.0 |