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Mathematics HS
Mathematics HS

Proof Example: The Irrationality of √ 2 During the lecture a student
Proof Example: The Irrationality of √ 2 During the lecture a student

MATHEMATICS ADMISSIONS TEST
MATHEMATICS ADMISSIONS TEST

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22 Mar 2015 - U3A Site Builder

Predicate Calculus - SIUE Computer Science
Predicate Calculus - SIUE Computer Science

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Class Notes Mathematics Physics 201-202.doc

PARADOX AND INTUITION
PARADOX AND INTUITION

Recognize and represent relationships between varying quantities
Recognize and represent relationships between varying quantities

Exercises: Sufficiently expressive/strong
Exercises: Sufficiently expressive/strong

Prime Numbers are Infinitely Many: Four Proofs from
Prime Numbers are Infinitely Many: Four Proofs from

... possibilities (Furinghetti & Somaglia, 1997). These levels do not reflect just practical educational issues, but imply important epistemological assumptions (Radford, 1997): for instance, the selection of historical data is epistemologically relevant, and several problems are connected with their in ...
Freshman Research Initiative: Research Methods
Freshman Research Initiative: Research Methods

Pre-Calculus Honors - Unit 2 Polynomial Functions
Pre-Calculus Honors - Unit 2 Polynomial Functions

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Every Day Is Mathematical

A simple proof of Parsons` theorem
A simple proof of Parsons` theorem

Maths basics - NSW Department of Education
Maths basics - NSW Department of Education

... We have seen that the four basic operations in mathematics are +, –,  and . A fifth operation, which is really just an extension of ‘multiply’, is so important that we should mention it here. This operation is the squaring operation, which means ‘multiply a number ...
Is `structure` a clear notion? - University of Illinois at Chicago
Is `structure` a clear notion? - University of Illinois at Chicago

The Language of Quantification in Mathematics
The Language of Quantification in Mathematics

Why the Sets of NF do not form a Cartesian-closed Category
Why the Sets of NF do not form a Cartesian-closed Category

one
one

Maths-2011_Leader_Symposium_Algebra_ppt
Maths-2011_Leader_Symposium_Algebra_ppt

An un-rigorous introduction to the incompleteness theorems
An un-rigorous introduction to the incompleteness theorems

On the paradoxes of set theory
On the paradoxes of set theory

Chapter 11: The Non-Denumerability of the Continuum
Chapter 11: The Non-Denumerability of the Continuum

... Limit: for any ε > 0, there exists a δ > 0 so that, if 0 < | x-a | < δ, then | f(x)-L | < ε ...
A counterexample to the infinite version of a
A counterexample to the infinite version of a

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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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