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Available on-line - Gert
Available on-line - Gert

... In 1967, Anderson [2] defined his system of relevant deontic logic as follows: take relevant system R, add a propositional constant V (“the violation” or “the bad thing”), and define O (“it is obligatory that”) by O A = ¬A → V , where → is relevant implication. This proposal naturally leads to the q ...
An Introduction to Elementary Set Theory
An Introduction to Elementary Set Theory

AI Principles, Semester 2, Week 2, Lecture 5 Propositional Logic
AI Principles, Semester 2, Week 2, Lecture 5 Propositional Logic

Rational Numbers - Abstractmath.org
Rational Numbers - Abstractmath.org

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Essential Elements Pacing Guide Middle School – Mathematics

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Algebra II v. 2016

... The table shows the world population of the Iberian Lynx in 2003 and 2004. If this trend continues and the population is decreasing exponentially, how many Iberian Lynx will there be in 2014? ...
Comparing and Converting Fractions and Mixed Numbers
Comparing and Converting Fractions and Mixed Numbers

Department for Analysis and Computational Number
Department for Analysis and Computational Number

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... As previously stated, one representation of the first n natural numbers is a  having n rows, in which the number of dots in the first triangular array of dots, row is 1, and the number of dots in each successive row increases by 1, so that in the nth row there are n dots. Copy the original triangu ...
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1)_C1_Algebra_and_Functions

Full text
Full text

... Prof. D.'E. Knuth of California Institute of Technology is working on a 3 volume book, The Analysis of Algorithms, which has 39 exercises at the end of the section which introduces the Fibonacci Sequence. However, the Fibonacci Sequence occurs in many different places, both as an operational tool, o ...
in solving problems
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... Show any derivative(s) that you need to find when solving the problems. The questions in this booklet are NOT in order of difficulty. Attempt all questions otherwise you may not provide enough evidence to achieve the required standard. If you need any more room for any answer, use the extra space pr ...
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Computer Science at Oxford

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... per serving. She also eats 5 servings of vegetables. If the rest of her daily intake is 870 calories, what is the average number of calories in each serving of vegetables? ...
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NONSTANDARD MODELS IN RECURSION THEORY

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Fundamental units and consecutive squarefull numbers,

Heyting-valued interpretations for Constructive Set Theory
Heyting-valued interpretations for Constructive Set Theory

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Lesson 1

Definability properties and the congruence closure
Definability properties and the congruence closure

< 1 ... 74 75 76 77 78 79 80 81 82 ... 187 >

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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