29(2)
... To understand Fibonacci's outstanding contributions to knowledge, it is necessary to know something of the age in which he lived and of the mathematics that preceded him. Indeed, a study of his writings reminds one of the history of pre-medieval mathematics in microcosm. In an age of great commercia ...
... To understand Fibonacci's outstanding contributions to knowledge, it is necessary to know something of the age in which he lived and of the mathematics that preceded him. Indeed, a study of his writings reminds one of the history of pre-medieval mathematics in microcosm. In an age of great commercia ...
Preferences and Unrestricted Rebut
... (possibly even the last one) is defeasible. Hence, if an argument restrictedly rebuts another argument then it also unrestrictedly rebuts it, but not vice versa. Forms of unrestricted rebut are applied in the formalism of Prakken and Sartor [16], the argumentation version of Nute’s Defeasible Logic ...
... (possibly even the last one) is defeasible. Hence, if an argument restrictedly rebuts another argument then it also unrestrictedly rebuts it, but not vice versa. Forms of unrestricted rebut are applied in the formalism of Prakken and Sartor [16], the argumentation version of Nute’s Defeasible Logic ...
Integers without large prime factors in short intervals: Conditional
... except that the bound for S(t) will be different. Remark 1. Recently Soundararajan [So10] has improved the result substantially on√RH alone. He proves, on RH, that there are Xα -smooth numbers in intervals of length c(α) X. Remark 2. Our proof shows that the number of Xα -smooth numbers in the inter ...
... except that the bound for S(t) will be different. Remark 1. Recently Soundararajan [So10] has improved the result substantially on√RH alone. He proves, on RH, that there are Xα -smooth numbers in intervals of length c(α) X. Remark 2. Our proof shows that the number of Xα -smooth numbers in the inter ...
Chapter 10. Sequences, etc. 10.1: Least upper bounds and greatest
... • If the terms in the sequence are all positive and are getting huge without any bound, we write limn→∞ an = ∞. Note that if the terms in the sequence are all positive then limn→∞ an = ∞ if and only if limn→∞ a1n = 0. Similarly, if the terms in a sequence are all negative then limn→∞ an = −∞ if and ...
... • If the terms in the sequence are all positive and are getting huge without any bound, we write limn→∞ an = ∞. Note that if the terms in the sequence are all positive then limn→∞ an = ∞ if and only if limn→∞ a1n = 0. Similarly, if the terms in a sequence are all negative then limn→∞ an = −∞ if and ...
ABSTRACT On the Goldbach Conjecture Westin King Director: Dr
... The authors employ several new methods to improve previous bounds, including a refinement of certain numerical estimates and a slight change to the general HardyLittlewood circle method. Usually with the circle method, the unit interval is broken into several disjoint subsets, for which Liu and Wang ...
... The authors employ several new methods to improve previous bounds, including a refinement of certain numerical estimates and a slight change to the general HardyLittlewood circle method. Usually with the circle method, the unit interval is broken into several disjoint subsets, for which Liu and Wang ...
Dedekind cuts of Archimedean complete ordered abelian groups
... DEFINITION 2. We will say that a Dedekind cut (X, Y) of an ordered group G is a Veronese cut of G, if for each positive d G there are x X and y Y for which y −x B d; if G is nondiscrete and every Veronese cut of G is a continuous cut we will say that G is Veronese continuous. Although these no ...
... DEFINITION 2. We will say that a Dedekind cut (X, Y) of an ordered group G is a Veronese cut of G, if for each positive d G there are x X and y Y for which y −x B d; if G is nondiscrete and every Veronese cut of G is a continuous cut we will say that G is Veronese continuous. Although these no ...
Modern Algebra I Section 1 · Assignment 3 Exercise 1. (pg. 27 Warm
... So d divides a + b . Recall that a + b is prime; by Theorem 2.7, it is irreducible. Since a + b is irreducible and a + b = d (x + y), by definition d = 1 or x + y = 1. If d = 1, then gcd (a, b ) = 1, and we are done. Otherwise, x + y = 1. We show that this assumption gives a contradiction. Substitut ...
... So d divides a + b . Recall that a + b is prime; by Theorem 2.7, it is irreducible. Since a + b is irreducible and a + b = d (x + y), by definition d = 1 or x + y = 1. If d = 1, then gcd (a, b ) = 1, and we are done. Otherwise, x + y = 1. We show that this assumption gives a contradiction. Substitut ...
CATEGORICAL MODELS OF FIRST
... case of classical categories) and also models where this equality does not hold; these non-idempotent models are intruiguing but not well understood. This thesis concentrates on the classical categories of Führmann and Pym, and extends their results to first-order LK, in the spirit of Lawvere [49] ...
... case of classical categories) and also models where this equality does not hold; these non-idempotent models are intruiguing but not well understood. This thesis concentrates on the classical categories of Führmann and Pym, and extends their results to first-order LK, in the spirit of Lawvere [49] ...
Proof Pearl: Defining Functions Over Finite Sets
... Alternative 2 above resembles the inductive definition of fold. Whichever alternative is chosen, we should only prove enough results about cardinality to allow the definition of fold : many lemmas about cardinality are instances of more general lemmas about set summation and can be obtained easily o ...
... Alternative 2 above resembles the inductive definition of fold. Whichever alternative is chosen, we should only prove enough results about cardinality to allow the definition of fold : many lemmas about cardinality are instances of more general lemmas about set summation and can be obtained easily o ...