• 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
fermat`s little theorem - University of Arizona Math
fermat`s little theorem - University of Arizona Math

Optimal acceptors and optimal proof systems
Optimal acceptors and optimal proof systems

B.Stat - Indian Statistical Institute
B.Stat - Indian Statistical Institute

NUMBER SYSTEM
NUMBER SYSTEM

Interpretability formalized
Interpretability formalized

... As with all sciences, mathematics aims at a better description and understanding of reality. Now, the logician asks: what is mathematical reality? Mathematics deals with numbers, functions, shapes, circles, sets, etc. But who has ever touched a number? Who has ever seen a real circle? The firm and u ...
Everything Else Being Equal: A Modal Logic for Ceteris Paribus
Everything Else Being Equal: A Modal Logic for Ceteris Paribus

... The paper is organized as follows. In Section 2, we present and discuss von Wright’s original work in preference logic, in order to motivate some of the notions we develop later, but also as a foundational standard against which we can evaluate our own results. In Section 3, we present a basic modal ...
Document
Document

... 4. The bleachers at a football game is 7/8 full, and half the fans are rooting for the home team. What fraction of the bleacher is rooting for the home team? ...
2014-2015 MATH Instructional Curriculum Plan Grade: 6
2014-2015 MATH Instructional Curriculum Plan Grade: 6

Document
Document

1 Non-deterministic Phase Semantics and the Undecidability of
1 Non-deterministic Phase Semantics and the Undecidability of

... directly into BBI and Kripke semantics, exactly as this was later done for Classical BI in [LarcheyWendling 2010]. But then, the intuition behind the encoding is arguably much more difficult to grasp. We also feel that the existence of the elementary fragment of ILL is important in itself, and in pa ...
Holt McDougal Algebra 2
Holt McDougal Algebra 2

MATH 1190 - Lili Shen
MATH 1190 - Lili Shen

Equivalent Fractions
Equivalent Fractions

Constraint Logic Programming with Hereditary Harrop Formula
Constraint Logic Programming with Hereditary Harrop Formula

Ethical Intuitionism: The Meaning of Meaning Senior
Ethical Intuitionism: The Meaning of Meaning Senior

7-4 - Humble ISD
7-4 - Humble ISD

... Most calculators calculate logarithms only in base 10 or base e (see Lesson 7-6). You can change a logarithm in one base to a logarithm in another base with the following formula. ...
Inductive Types in Constructive Languages
Inductive Types in Constructive Languages

here
here

... Proposition 2. Assume the numbers r, s, and t are as in Lemma 1. If either (i). 16 6= r ∈ N, or (ii). rn ∈ Q \ Q for all n ∈ N, then at least one of the numbers s and t is transcendental. In [15, Conjecture 3.7] we made the following prediction. Conjecture 2. A stronger conclusion holds in Propositi ...
Pre-Calculus - Lee County School District
Pre-Calculus - Lee County School District

Set Theory for Computer Science (pdf )
Set Theory for Computer Science (pdf )

The Deduction Rule and Linear and Near
The Deduction Rule and Linear and Near

MAD2104 Course Notes - FSU Math
MAD2104 Course Notes - FSU Math

Many-Valued Logic
Many-Valued Logic

Pacing_Guide_6th_Grade - ExploreLearning PD Blog
Pacing_Guide_6th_Grade - ExploreLearning PD Blog

Document
Document

< 1 2 3 4 5 6 7 8 9 ... 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