Modal logic and the approximation induction principle
... image-finite LTSs, but that do have the Hennessy–Milner property. That is, models where the modal equivalence ∼HML coincides with bisimulation equivalence. This led to the notion of modally saturated processes; an LTS is M-saturated if for all states s and all O ⊆ HML, whenever every finite subset o ...
... image-finite LTSs, but that do have the Hennessy–Milner property. That is, models where the modal equivalence ∼HML coincides with bisimulation equivalence. This led to the notion of modally saturated processes; an LTS is M-saturated if for all states s and all O ⊆ HML, whenever every finite subset o ...
1.1. RELATIONS Defining relations as sets of ordered pairs
... If the number of ordered pairs in the set defining a relation is very large or even infinite then the best way to describe the relation is through using an equation or an inequality. 1.1.11. EXAMPLE. Let us consider a relation described by the equation x4 + y 2 = 10. The number 1 is related to the n ...
... If the number of ordered pairs in the set defining a relation is very large or even infinite then the best way to describe the relation is through using an equation or an inequality. 1.1.11. EXAMPLE. Let us consider a relation described by the equation x4 + y 2 = 10. The number 1 is related to the n ...
Finite and Infinite Sets
... may seem simple for finite sets, but as we will see, this idea has surprising consequences when we deal with infinite sets. (We will soon provide precise definitions for finite and infinite sets.) Technical Note: The three properties we proved in Theorem 9.1 in Preview Activity 2 are very similar to ...
... may seem simple for finite sets, but as we will see, this idea has surprising consequences when we deal with infinite sets. (We will soon provide precise definitions for finite and infinite sets.) Technical Note: The three properties we proved in Theorem 9.1 in Preview Activity 2 are very similar to ...
10-01-2014 Dear Teachers,
... Plane Isometries, Direct products & finitely generated Abelian Groups, Factor Groups, Factor-Group Computations and Simple Groups, Group action on a set, Applications of G-set to counting. [Sections 12, 11, 4, 14, 15, 16, 17] Module - II Isomorphism theorems, Series of groups, (Omit Butterfly Lemma ...
... Plane Isometries, Direct products & finitely generated Abelian Groups, Factor Groups, Factor-Group Computations and Simple Groups, Group action on a set, Applications of G-set to counting. [Sections 12, 11, 4, 14, 15, 16, 17] Module - II Isomorphism theorems, Series of groups, (Omit Butterfly Lemma ...
Advanced Logic —
... P ROOF. Suppose IND is true, but for a reductio, suppose that LNP is not. Then there is some subset B ⊆ N such that: (1) B is not empty; and (2) B has no least element. Let A = N\B. Clearly 0 ∈ / B (for then 0 would be the least element), so 0 ∈ A. Moreover, since B has no least element, this just m ...
... P ROOF. Suppose IND is true, but for a reductio, suppose that LNP is not. Then there is some subset B ⊆ N such that: (1) B is not empty; and (2) B has no least element. Let A = N\B. Clearly 0 ∈ / B (for then 0 would be the least element), so 0 ∈ A. Moreover, since B has no least element, this just m ...
Chapter 4 Number theory - School of Mathematical and Computer
... about first as children are the source of some of mathematics most difficult and interesting questions. ...
... about first as children are the source of some of mathematics most difficult and interesting questions. ...
a review of prime patterns - Mathematics
... prime numbers. Since the Greeks, prime numbers have been found to apply to more than just pure mathematics, but have applications in cryptography and even animation. As of now, there is no one pattern that can find all prime numbers but there are many other patterns that can find finite sequences of ...
... prime numbers. Since the Greeks, prime numbers have been found to apply to more than just pure mathematics, but have applications in cryptography and even animation. As of now, there is no one pattern that can find all prime numbers but there are many other patterns that can find finite sequences of ...
Lecture Notes - jan.ucc.nau.edu
... Proof by Contradiction: Example • Theorem: There exists an infinite number of prime numbers. • Proof (courtesy of Euclid): 1. Assume that there are a finite number of primes. 2. Then there is a largest prime, p. Consider the number q = (2x3x5x7x...xp)+1. q is one more than the product of all primes ...
... Proof by Contradiction: Example • Theorem: There exists an infinite number of prime numbers. • Proof (courtesy of Euclid): 1. Assume that there are a finite number of primes. 2. Then there is a largest prime, p. Consider the number q = (2x3x5x7x...xp)+1. q is one more than the product of all primes ...
Chapter 1
... Adding two positive integers: Add the digits and keep the sign Adding two negative integers: Add the digits and keep the sign Adding a positive and a negative integer: Subtract the smaller from the larger digit (disregarding the signs) and keep the sign of the larger digit (if the sign is disr ...
... Adding two positive integers: Add the digits and keep the sign Adding two negative integers: Add the digits and keep the sign Adding a positive and a negative integer: Subtract the smaller from the larger digit (disregarding the signs) and keep the sign of the larger digit (if the sign is disr ...
Proof, Sets, and Logic - Department of Mathematics
... the i operation. It is certainly a valid point which is being made, but I would like to say it neatly. It is nice to get to it before one tries to construct NF(U); thus one does not naturally wander into the NF problem. July 9, 2009: I am editing the text again, much later, with an eye to starting t ...
... the i operation. It is certainly a valid point which is being made, but I would like to say it neatly. It is nice to get to it before one tries to construct NF(U); thus one does not naturally wander into the NF problem. July 9, 2009: I am editing the text again, much later, with an eye to starting t ...
