• Study Resource
  • Explore
    • Arts & Humanities
    • Business
    • Engineering & Technology
    • Foreign Language
    • History
    • Math
    • Science
    • Social Science

    Top subcategories

    • Advanced Math
    • Algebra
    • Basic Math
    • Calculus
    • Geometry
    • Linear Algebra
    • Pre-Algebra
    • Pre-Calculus
    • Statistics And Probability
    • Trigonometry
    • other →

    Top subcategories

    • Astronomy
    • Astrophysics
    • Biology
    • Chemistry
    • Earth Science
    • Environmental Science
    • Health Science
    • Physics
    • other →

    Top subcategories

    • Anthropology
    • Law
    • Political Science
    • Psychology
    • Sociology
    • other →

    Top subcategories

    • Accounting
    • Economics
    • Finance
    • Management
    • other →

    Top subcategories

    • Aerospace Engineering
    • Bioengineering
    • Chemical Engineering
    • Civil Engineering
    • Computer Science
    • Electrical Engineering
    • Industrial Engineering
    • Mechanical Engineering
    • Web Design
    • other →

    Top subcategories

    • Architecture
    • Communications
    • English
    • Gender Studies
    • Music
    • Performing Arts
    • Philosophy
    • Religious Studies
    • Writing
    • other →

    Top subcategories

    • Ancient History
    • European History
    • US History
    • World History
    • other →

    Top subcategories

    • Croatian
    • Czech
    • Finnish
    • Greek
    • Hindi
    • Japanese
    • Korean
    • Persian
    • Swedish
    • Turkish
    • other →
 
Profile Documents Logout
Upload
Solutions - TeacherWeb
Solutions - TeacherWeb

CHAPTER 8 Hilbert Proof Systems, Formal Proofs, Deduction
CHAPTER 8 Hilbert Proof Systems, Formal Proofs, Deduction

... possible to ”reverse” their use; to use them in the reverse manner in order to search for proofs, and we were able to do so in a blind, fully automatic way. We were able to conduct an argument of the type: if this formula has a proof the only way to construct it is from such and such formulas by th ...
Hausdorff dimension and Diophantine approximation Yann
Hausdorff dimension and Diophantine approximation Yann

Geodesics, volumes and Lehmer`s conjecture Mikhail Belolipetsky
Geodesics, volumes and Lehmer`s conjecture Mikhail Belolipetsky

Total interval numbers of complete r
Total interval numbers of complete r

... each set of F as a vertex and joining two vertices with an edge if their corresponding sets intersect. The family of sets is called an intersection representation of its intersection graph. For an intersection representation F of a graph G = (V; E), we often use a bijection f from V to F to represen ...
Chapter 1
Chapter 1

Lesson 24 - EngageNY
Lesson 24 - EngageNY

Chapter 6
Chapter 6

Second-Order Logic of Paradox
Second-Order Logic of Paradox

... This conjunction is true (though also, because of its universally quantified Second-order conjunct, also false: it takes the value Both) in Secondorder LP models with the genuine natural numbers as individuals and in many, though not all, of the finite inconsistent models described in Priest [12]: t ...
Truth Value Solver: A Software for Calculating Truth Value with
Truth Value Solver: A Software for Calculating Truth Value with

RECURSIVE REAL NUMBERS 784
RECURSIVE REAL NUMBERS 784

Q. 1 – Q. 5 carry one mark each.
Q. 1 – Q. 5 carry one mark each.

... ming numberr of people innfected with h rabies in Inndia has beenn flagged by y the World Heaalth Organizzation as a soource of conncern. It is esstimated thatt inoculatingg 70% of petts and stray doggs against rabbies can leadd to a significcant reductio on in the num mber of peoplle infected with ...
Axiomatic Method Logical Cycle Starting Place Fe
Axiomatic Method Logical Cycle Starting Place Fe

Lecture notes #2 - inst.eecs.berkeley.edu
Lecture notes #2 - inst.eecs.berkeley.edu

HSC Mathematics Extension 2
HSC Mathematics Extension 2

Secondary English Language Arts
Secondary English Language Arts

Standard/Benchmark/Indicator
Standard/Benchmark/Indicator

Arithmetic Circuits - inst.eecs.berkeley.edu
Arithmetic Circuits - inst.eecs.berkeley.edu

Unit 1 – Square Roots and Surface Area Section 1.1 – Square Roots
Unit 1 – Square Roots and Surface Area Section 1.1 – Square Roots

23-ArithI - University of California, Berkeley
23-ArithI - University of California, Berkeley

Lecture notes #2: Proofs - EECS: www
Lecture notes #2: Proofs - EECS: www

Full text
Full text

la maison ou jai grandi
la maison ou jai grandi

First-Order Proof Theory of Arithmetic
First-Order Proof Theory of Arithmetic

F - Teaching-WIKI
F - Teaching-WIKI

< 1 ... 48 49 50 51 52 53 54 55 56 ... 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.
  • studyres.com © 2025
  • DMCA
  • Privacy
  • Terms
  • Report