proof terms for classical derivations
... of p. The second assumed p twice (tagging these assumptions with x and y), conjoined their result (in that order) and disharged them in turn (also in that order). Seeing this, you may realise that there are two other proofs of the same formula. One where the conjuncts are formed in the other order ( ...
... of p. The second assumed p twice (tagging these assumptions with x and y), conjoined their result (in that order) and disharged them in turn (also in that order). Seeing this, you may realise that there are two other proofs of the same formula. One where the conjuncts are formed in the other order ( ...
Discrete Mathematics for Computer Science Some Notes
... degree in computer science end up with jobs where mathematical skills seem basically of no use,1 one may ask why these students should take such a course. And if they do, what are the most basic notions that they should learn? As to the first question, I strongly believe that all computer science st ...
... degree in computer science end up with jobs where mathematical skills seem basically of no use,1 one may ask why these students should take such a course. And if they do, what are the most basic notions that they should learn? As to the first question, I strongly believe that all computer science st ...
3. Problem Solving Methods in Combinatorics - An
... “n factorial”. We define 0! as 1. An ordering of a list is also called a permutation of the list. In the following chapters we will study permutations from another point of view. Example 1.1.6 If A is a set with n elements, how many subsets does it have? Solution To solve this example the event we w ...
... “n factorial”. We define 0! as 1. An ordering of a list is also called a permutation of the list. In the following chapters we will study permutations from another point of view. Example 1.1.6 If A is a set with n elements, how many subsets does it have? Solution To solve this example the event we w ...
material - Department of Computer Science
... on. If you claim something is true, you should explain why it is true; that is you should prove it. In some cases an idea is introduced before you have the tools to prove it, or the proof of something will add nothing to your understanding. In such problems there is a remark telling you not to bothe ...
... on. If you claim something is true, you should explain why it is true; that is you should prove it. In some cases an idea is introduced before you have the tools to prove it, or the proof of something will add nothing to your understanding. In such problems there is a remark telling you not to bothe ...
Modal fixpoint logic: some model theoretic questions
... Now, from what we have seen, the µ-calculus seems a well-suited specification language, as it combines a great expressive power and manageable decision procedures. But there is a drawback: the µ-calculus is probably not the most understandable way to specify behaviors. Most people would have a diffi ...
... Now, from what we have seen, the µ-calculus seems a well-suited specification language, as it combines a great expressive power and manageable decision procedures. But there is a drawback: the µ-calculus is probably not the most understandable way to specify behaviors. Most people would have a diffi ...
Problems on Discrete Mathematics1 (Part I)
... correct. But, in general, we are not able to do so because the domain is usually an infinite set, and even worse, the domain can be uncountable, e.g., real numbers. To overcome this problem, we divide the domain into several categories and make sure that those categories cover the domain. Then we ex ...
... correct. But, in general, we are not able to do so because the domain is usually an infinite set, and even worse, the domain can be uncountable, e.g., real numbers. To overcome this problem, we divide the domain into several categories and make sure that those categories cover the domain. Then we ex ...
Modular Construction of Complete Coalgebraic Logics
... constant sets and composition. A recent survey of existing probabilistic models of systems [3] identified no less than eight probabilistic system types of interest, all of which can be written as such combinations. This paper derives logics and proof systems for these probabilistic system types, usi ...
... constant sets and composition. A recent survey of existing probabilistic models of systems [3] identified no less than eight probabilistic system types of interest, all of which can be written as such combinations. This paper derives logics and proof systems for these probabilistic system types, usi ...
Chapter 2 pdf
... Polynomial functions are classified by degree. For instance, a constant function has degree 0 and a linear function has degree 1. In this section, you will study second-degree polynomial functions, which are called quadratic functions. For instance, each of the following functions is a quadratic fun ...
... Polynomial functions are classified by degree. For instance, a constant function has degree 0 and a linear function has degree 1. In this section, you will study second-degree polynomial functions, which are called quadratic functions. For instance, each of the following functions is a quadratic fun ...
Distribution of Prime Numbers
... Note that σ(u) and u are integers and σ(u) > u. Hence u/(2m − 1) ∈ N and is a divisor of u. Since m > 1, we have 2m − 1 > 1, and so u/(2m − 1) '= u. It now follows from (3) that σ(u) is equal to the sum of two of its positive divisors. But σ(u) is equal to the sum of all its positive divisors. Hence ...
... Note that σ(u) and u are integers and σ(u) > u. Hence u/(2m − 1) ∈ N and is a divisor of u. Since m > 1, we have 2m − 1 > 1, and so u/(2m − 1) '= u. It now follows from (3) that σ(u) is equal to the sum of two of its positive divisors. But σ(u) is equal to the sum of all its positive divisors. Hence ...
39(5)
... Requests for reprint permission should be directed to the editor. However, general permission is granted to members of The Fibonacci Association for noncommercial reproduction of a limited quantity of individual articles (in whole or in part) provided complete reference is made to the source. Annual ...
... Requests for reprint permission should be directed to the editor. However, general permission is granted to members of The Fibonacci Association for noncommercial reproduction of a limited quantity of individual articles (in whole or in part) provided complete reference is made to the source. Annual ...
Sequences - UC Davis Mathematics
... A sequence converges if it converges to some limit x ∈ R, otherwise it diverges. Although we don’t show it explicitly in the definition, N is allowed to depend on . Typically, the smaller we choose , the larger we have to make N . One way to view a proof of convergence is as a game: If I give you ...
... A sequence converges if it converges to some limit x ∈ R, otherwise it diverges. Although we don’t show it explicitly in the definition, N is allowed to depend on . Typically, the smaller we choose , the larger we have to make N . One way to view a proof of convergence is as a game: If I give you ...