By this time, you are probably not surprised to see that there is a very general form of Ramsey's theorem. We have a bounded number of bins or colors and we are placing the subsets of a fixed size into these categories.
Ramsey's Theorem
By this time, you are probably not surprised to see that there is a very general form of Ramsey's theorem. We have a bounded number of bins or colors and we are placing the subsets of a fixed size into these categories. The conclusion is that there is a large set which is treated uniformly.
Here's the formal statement.
We don't include the proof of this general statement here, but the more ambitious students may attempt it on their own. Note that the case \(s=1\) is just the , while the case \(s=r=2\) is just . An argument using double induction is required for the proof in the general case. The first induction is on \(r\) and the second is on \(s\).
Sasa
Hakuna kifaa cha kupigia hesabu kinachoweza kufanya hesabu, lakini kifaa hicho kinaweza kutumiwa katika hesabu.
Keep your own working
Akaunti la bure laongezea mambo makuu juu ya kila somo, rekodi ya yale ambayo umemaliza, matatizo yako ya kutatua katika sehemu moja, na mtunzaji unayeweza kuuliza juu ya ukurasa huu.
Vaa alama yoyote ya ufafanuzi kamili, picha, na maana ya kila herufi.
Maana ya kila sehemu
Wazia hilo
Inastahili Kujua
Vielelezo
Pia, ufafanuzi huo ulitumiwa
Maswali ambayo watu huuliza
What is the difference between probability and statistics?
Probability goes from a known model to what the data should look like; statistics goes from data back to the model. Probability theory is the deductive half.
What does the law of large numbers promise?
That the average of many independent samples converges to the expected value. It says nothing about any single trial.
Sehemu za ukurasa huu zimebadilishwa kutoka kwa
Keller & Trotter, Applied Combinatorics (CC BY-SA 4.0).
Tumekamatwa na kukosolewa tena hapa; makosa ni yetu.