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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.
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 \(s\).
Энди сизлар Буни ҳисоблаш учун ҳисоблагич керак эмас, лекин унинг қисмлари ҳисоблаш мумкин. Қуйида бирор нарсани синаб кўринг ёки ўзингиз ёзинг.
Бепул ҳисоб ҳар бир дарсга ёзув қўшиб беради, сиз тугатган нарсалар ва ҳал қилинган масалалар бир жойда қайд этилади ва сиз бу саҳифа ҳақида устоздан сўрашингиз мумкин. Математика ўзида очиқ бўлиб, унга кириш ёки киришни истамаган ҳар кимга очиқ.
Ройхатдан ўтиш КиришБу ерда қўлланилган белгилар
Барча белгилар учун тўлиқ таъриф, сурат ва ҳар бир ҳарфнинг маъносини кўриш учун белгини босинг.
Одамлар сўрайдиган саволлар
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.
Бу саҳифанинг қисмлари Keller & Trotter, Applied Combinatorics (CC BY-SA 4.0). (Ушбу оятда Аллоҳ таоло Пайғамбаримиз Муҳаммадга (с. а. в.) Қуръони Каримни туширишни амр қилмоқда.)
Кўпроқ Probability Theory
Sample spaces and the axiomsRandom variables and expectationThe common distributionsThe law of large numbers and the central limit theorem