Sets+ combinatorics
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Sets+ combinatorics
Lecture notes Sets and CombinatoricsThese lecture notes are based on earlier texts by Marcel van de Vel, André Ran, Wouter Kager, and other staff memb Sets+ combinatorics bers of the Department of Mathematics at the Vrije Universiteit Amsterdam.Contents1Basic concepts of set theory'11.1Principles of set theory11.2Fundamental set operations413The algebra of sets71.4Collections of sets112Standard sample spaces152.1Sets in probability theory152.2Draws without replacemen Sets+ combinatorics t / with order1723Draws without replacement/ without order202.4Draws with replacement / with order222.5Draws with replacement/ without order243CombinaSets+ combinatorics
torial analysis293.1rhe principle of mathematical induction293.2The binomial and multinomial theorems323.3Combinatorial principles of counting374 FuncLecture notes Sets and CombinatoricsThese lecture notes are based on earlier texts by Marcel van de Vel, André Ran, Wouter Kager, and other staff memb Sets+ combinatorics assignmentsIndex55571 Basic concepts of set theory1.1 Principles of set theoryhl mathematics, a srt Is an (unordered) collection of elements, such as the collection of all integers greater than 0 and less than 10, or that of all even numbers. Such a sei is often indicated by a listing of the element Sets+ combinatorics s inside airly brackets, with the elements being separated by commas. Thus we can write the above two sets as(1,2,3,...,9| and (2,4,6,...|.In accordanSets+ combinatorics
ce with good practice, we are using here to indicate that the listing of the foregoing elements is to be continued in the same pattern. We agree that Lecture notes Sets and CombinatoricsThese lecture notes are based on earlier texts by Marcel van de Vel, André Ran, Wouter Kager, and other staff memb Sets+ combinatorics lear that some other continuation is intended. By |1,..., 6) we thus mean all integers from 1 through 6, but by {0,2,4,...,12| only thet’WH numbers from 0 through 12.rhe following sets are assumed to be known from I’re-Lniversily Education:•N= {1,2,3,...}theset ofnal ural numbers-,•z-{...,-2,-1,0,1, Sets+ combinatorics 2,...} the set of integers;Lecture notes Sets and CombinatoricsThese lecture notes are based on earlier texts by Marcel van de Vel, André Ran, Wouter Kager, and other staff membLecture notes Sets and CombinatoricsThese lecture notes are based on earlier texts by Marcel van de Vel, André Ran, Wouter Kager, and other staff membGọi ngay
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