full - CS.Duke
... where the primes are in nondecreasing order is unique. (This is part of the fundamental theorem of arithmetic. The other part, which asserts that every positive integer has a prime factorization into primes, will be proved in Section 5.2.) Proof: (by contradiction) Suppose that the positive integer ...
... where the primes are in nondecreasing order is unique. (This is part of the fundamental theorem of arithmetic. The other part, which asserts that every positive integer has a prime factorization into primes, will be proved in Section 5.2.) Proof: (by contradiction) Suppose that the positive integer ...
ON TOPOLOGICAL NUMBERS OF GRAPHS 1. Introduction
... bijective set-valued function f : V ∪E → 2X \{∅} such that f (u, v) = f (u)⊕f (v) for every (u, v) ∈ E. Later, Mollard and Payan [11] settled two conjectures about set-graceful graphs suggested by Acharya in [1]. Hegde [8] obtained certain necessary conditions for a graph to have set-graceful and se ...
... bijective set-valued function f : V ∪E → 2X \{∅} such that f (u, v) = f (u)⊕f (v) for every (u, v) ∈ E. Later, Mollard and Payan [11] settled two conjectures about set-graceful graphs suggested by Acharya in [1]. Hegde [8] obtained certain necessary conditions for a graph to have set-graceful and se ...
Forking in simple theories and CM-triviality Daniel Palacín Cruz
... equivalence relations. Nevertheless, every theory with the strict order property has a hyperimaginary which is not eliminable [2]. Therefore, there are examples of small theories that do not eliminate hyperimaginaries; but the question is still open for small simple theories. In addition, there is a ...
... equivalence relations. Nevertheless, every theory with the strict order property has a hyperimaginary which is not eliminable [2]. Therefore, there are examples of small theories that do not eliminate hyperimaginaries; but the question is still open for small simple theories. In addition, there is a ...
20(2)
... university teachers and students,, These articles should be lively and well motivated, with innovative ideas that develop enthusiasm for number sequences or the exploration of number facts. Articles should be submitted in the format of the current issues of the Quarterly. They should be typewritten ...
... university teachers and students,, These articles should be lively and well motivated, with innovative ideas that develop enthusiasm for number sequences or the exploration of number facts. Articles should be submitted in the format of the current issues of the Quarterly. They should be typewritten ...
Complete Notes
... to determine when (p) is a product of two principal ideals in OQ(√−n) . The first part of the semester will be motivated by these questions, though we shall spend a lot of our time pursuing related questions and topics along the way. In other words, our goal is not so much to seek a definitive answ ...
... to determine when (p) is a product of two principal ideals in OQ(√−n) . The first part of the semester will be motivated by these questions, though we shall spend a lot of our time pursuing related questions and topics along the way. In other words, our goal is not so much to seek a definitive answ ...
Elementary Number Theory, A Computational Approach
... For us an algorithm is a finite sequence of instructions that can be followed to perform a specific task, such as a sequence of instructions in a computer program, which must terminate on any valid input. The word “algorithm” is sometimes used more loosely (and sometimes more precisely) than defined ...
... For us an algorithm is a finite sequence of instructions that can be followed to perform a specific task, such as a sequence of instructions in a computer program, which must terminate on any valid input. The word “algorithm” is sometimes used more loosely (and sometimes more precisely) than defined ...
l - OPUS at UTS - University of Technology Sydney
... Every year, Mathematics Awareness Week celebrates the richness and relevance of mathematics and provides an excellent opportunity to convey this message through local events. During a week-long celebration from Sunday, 23 April - Saturday, 29 April 1995, the festivities will highlight "MATHEMATICS A ...
... Every year, Mathematics Awareness Week celebrates the richness and relevance of mathematics and provides an excellent opportunity to convey this message through local events. During a week-long celebration from Sunday, 23 April - Saturday, 29 April 1995, the festivities will highlight "MATHEMATICS A ...
Mathematical proof
In mathematics, a proof is a deductive argument for a mathematical statement. In the argument, other previously established statements, such as theorems, can be used. In principle, a proof can be traced back to self-evident or assumed statements, known as axioms. Proofs are examples of deductive reasoning and are distinguished from inductive or empirical arguments; a proof must demonstrate that a statement is always true (occasionally by listing all possible cases and showing that it holds in each), rather than enumerate many confirmatory cases. An unproved proposition that is believed true is known as a conjecture.Proofs employ logic but usually include some amount of natural language which usually admits some ambiguity. In fact, the vast majority of proofs in written mathematics can be considered as applications of rigorous informal logic. Purely formal proofs, written in symbolic language instead of natural language, are considered in proof theory. The distinction between formal and informal proofs has led to much examination of current and historical mathematical practice, quasi-empiricism in mathematics, and so-called folk mathematics (in both senses of that term). The philosophy of mathematics is concerned with the role of language and logic in proofs, and mathematics as a language.