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 \(s\).
اب آپ
هيک کليچر اس کو حل نہیں کر سکتا ، ليکن اس کے ٹکڑے حسابي هے. نيچے سے کو ئي کوشش کريں يا خود کو ٹائپ کريں
آپ کے اپنے کام رکھیں
مفت اکاؤنٹ تمام درسوں پر نوٹ شامل کر تا هے ، آپ نے جو ختم کر يا هے اس کا ريکورڈ ، آپ کے حل کيے گئے مسئلے ایک جگہ پر اور آپ اس صفحے کے بارے ميں سوال کر سکتے هيں تو تيرچر ريتھ ميں خود تمام لوگوں کے ليے کھلا هے ، خواہ آپ داخل هے يا نہيں
تمام تعريف کے ليے ، تصوير کے ليے اور اس ميں ہر حروف کا مطلب کے ليے کو ئي علامت کو ٹک کريں
ہر حصے کا مطلب کیا ہے
اس کو تصور کریں
جاننے کے قابل
مثالیں
اس وضاحت میں بھی استعمال کیا جاتا ہے
سوالات لوگ پوچھتے ہیں
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.