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Here - Math-Boise State
Here - Math-Boise State



Essentials Of Symbolic Logic
Essentials Of Symbolic Logic

X - University of California, Santa Barbara
X - University of California, Santa Barbara

The Farey Sequence and Its Niche(s)
The Farey Sequence and Its Niche(s)

Advanced Internet Technologies
Advanced Internet Technologies

Foundations of Databases - Free University of Bozen
Foundations of Databases - Free University of Bozen

properties of rational expressions
properties of rational expressions

standards addressed in this unit
standards addressed in this unit

the existence of fibonacci numbers in the algorithmic generator for
the existence of fibonacci numbers in the algorithmic generator for

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preliminary version

THE ARITHMETIC LARGE SIEVE WITH AN APPLICATION TO THE
THE ARITHMETIC LARGE SIEVE WITH AN APPLICATION TO THE

Rational and irrational numbers
Rational and irrational numbers

Classical Propositional Logic
Classical Propositional Logic

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- ScholarWorks@GVSU

Propositional Logic
Propositional Logic

logic for computer science - Institute for Computing and Information
logic for computer science - Institute for Computing and Information

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On perturbations of continuous structures - HAL

- ScholarWorks@GVSU
- ScholarWorks@GVSU

CS 208: Automata Theory and Logic
CS 208: Automata Theory and Logic

Proof
Proof

... We could try indirect proof also, but in this case, it is a little simpler to just use proof by contradiction (very similar to indirect). So, what are we trying to show? Just that x + y is irrational. That is, :9i, j: (x + y ) = ji . What happens if we hypothesize the negation of this statement? ...
ON PERTURBATIONS OF CONTINUOUS STRUCTURES
ON PERTURBATIONS OF CONTINUOUS STRUCTURES

An Institution-Independent Generalization of Tarski`s Elementary
An Institution-Independent Generalization of Tarski`s Elementary

PDF - University of Kent
PDF - University of Kent

Programming in Logic Without Logic Programming
Programming in Logic Without Logic Programming

... In KELPS, states are represented by sets of atomic sentences (also called ground atoms, facts or fluents). Events are also represented by atomic sentences. Such sets of atomic sentences can be understood either syntactically as theories or sematically as model-theoretic structures. It is this second ...
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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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