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Blog #2 - Professor Fekete
Blog #2 - Professor Fekete

... of March 7, 2010, entitled FINDING YOUR ROOTS (blog #230). The gap was left for the sake of simplicity of presentation. The reader may pick up the thread by going to the fourth paragraph of my earlier blog. We have seen that, although the two direct operations addition and multiplication could alway ...
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ARISTOTLE`S SYLLOGISM: LOGIC TAKES FORM

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Introduction to Discrete Mathematics

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Welcome to 6th Grade Ma+h

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Natural deduction for predicate logic

The structure of the Fibonacci numbers in the modular ring Z5
The structure of the Fibonacci numbers in the modular ring Z5

The logic and mathematics of occasion sentences
The logic and mathematics of occasion sentences

... occasion sentences their rightful central place in semantics and secondly, taking these as the basic propositional elements in the logical analysis of language, to contribute to the development of an adequate logic of occasion sentences and a mathematical (Boolean) foundation for such a logic, thus ...
Handout 1 - Birkbeck
Handout 1 - Birkbeck

... You may argue that + is ambiguous because it means the sign of a positive number and also the operation of ADD. However the ambiguity is removed by the context. Writing 2 + 3, clearly uses + as ADD and writing +4 clearly uses + as the positive sign. It is DUALITY of usage not ambiguity in usage. ...
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XR3a

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Chapter Summary and Summary Exercises

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On the Infinitude of the Prime Numbers

Verification and Specification of Concurrent Programs
Verification and Specification of Concurrent Programs

... expressed in terms of these actions. To prove that one abstract program Π1 implements another abstract program Π2 , one must prove: 1. Every possible initial state of Π1 is a possible initial state of Π2 . 2. Every step allowed by Π1 ’s next-state relation is allowed by Π2 ’s next-state relation—a c ...
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Transfinite progressions: A second look at completeness.

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Grade K - PA Standards to CCSS

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UCLACurtisTalk

Unit 10 - Georgia Standards
Unit 10 - Georgia Standards

... • Understand that the basic properties of numbers continue to hold with polynomials During the school-age years, students must repeatedly extend their conception of numbers. From counting numbers to fractions, students are continually updating their use and knowledge of numbers. In Grade 8, students ...
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Chapter 1

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Weyl`s Predicative Classical Mathematics as a Logic
Weyl`s Predicative Classical Mathematics as a Logic

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Foundations of mathematics

Foundations of mathematics is the study of the logical and philosophical basis of mathematics, or, in a broader sense, the mathematical investigation of what underlies the philosophical theories concerning the nature of mathematics. In this latter sense, the distinction between foundations of mathematics and philosophy of mathematics turns out to be quite vague. Foundations of mathematics can be conceived as the study of the basic mathematical concepts (number, geometrical figure, set, function, etc.) and how they form hierarchies of more complex structures and concepts, especially the fundamentally important structures that form the language of mathematics (formulas, theories and their models giving a meaning to formulas, definitions, proofs, algorithms, etc.) also called metamathematical concepts, with an eye to the philosophical aspects and the unity of mathematics. The search for foundations of mathematics is a central question of the philosophy of mathematics; the abstract nature of mathematical objects presents special philosophical challenges.The foundations of mathematics as a whole does not aim to contain the foundations of every mathematical topic.Generally, the foundations of a field of study refers to a more-or-less systematic analysis of its most basic or fundamental concepts, its conceptual unity and its natural ordering or hierarchy of concepts, which may help to connect it with the rest of human knowledge. The development, emergence and clarification of the foundations can come late in the history of a field, and may not be viewed by everyone as its most interesting part.Mathematics always played a special role in scientific thought, serving since ancient times as a model of truth and rigor for rational inquiry, and giving tools or even a foundation for other sciences (especially physics). Mathematics' many developments towards higher abstractions in the 19th century brought new challenges and paradoxes, urging for a deeper and more systematic examination of the nature and criteria of mathematical truth, as well as a unification of the diverse branches of mathematics into a coherent whole.The systematic search for the foundations of mathematics started at the end of the 19th century and formed a new mathematical discipline called mathematical logic, with strong links to theoretical computer science.It went through a series of crises with paradoxical results, until the discoveries stabilized during the 20th century as a large and coherent body of mathematical knowledge with several aspects or components (set theory, model theory, proof theory, etc.), whose detailed properties and possible variants are still an active research field.Its high level of technical sophistication inspired many philosophers to conjecture that it can serve as a model or pattern for the foundations of other sciences.
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