• 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
Logical Inference and Mathematical Proof
Logical Inference and Mathematical Proof

- ScholarWorks@GVSU
- ScholarWorks@GVSU

... that every time we add two odd integers, the sum is an even integer. However, it is not possible to test every pair of odd integers, and so we can only say that the conjecture appears to be true. (We will prove that this statement is true in the next section.)  Use of prior knowledge. This also is ...
Mathematical induction Elad Aigner-Horev
Mathematical induction Elad Aigner-Horev

AN INTRODUCTION TO LOGIC
AN INTRODUCTION TO LOGIC

Full text
Full text

a(x)
a(x)

... to 8 with no difficulty, and of her own accord discovered that each number could be given with various different divisions, this leaving no doubt that she was consciously thinking each number. In fact, she did mental arithmetic, although unable, like humans, to name the numbers. But she learned to r ...
Argument construction and reinstatement in logics for
Argument construction and reinstatement in logics for

... reasoning about the priorities among defeasible rules. The system is provided in Kowalski and Toni (1996) only with a semantics, but it inherits the proof theory of Dung et al. (1996), and again, it is motivated primarily with examples involving legal reasoning. Although the intuitions underlying ma ...
Cryptography and Network Security 4/e
Cryptography and Network Security 4/e

L04 - Number Theory and Finite Fields
L04 - Number Theory and Finite Fields

Propositional Logic and Methods of Inference
Propositional Logic and Methods of Inference

... is valid no matter what is substituted for X, Y, and Z Separating the form from the semantics, the validity of an argument can be considered objectively, without prejudice caused by the ...
Mathematics Learning Progressions August 2014
Mathematics Learning Progressions August 2014

Chapter 1 Number Systems
Chapter 1 Number Systems

1 The Natural Numbers
1 The Natural Numbers

Chapter 1 Number Systems
Chapter 1 Number Systems

... A number line can be used to show the numbers of a set in their relationship to each other. Each number is represented by a point on the line called the graph of the number. There are two standard forms of the number line that we use. One a vertical number line (as pictured left), such as one seen o ...
Document
Document



Modal Logic - Web Services Overview
Modal Logic - Web Services Overview

LOGIC I 1. The Completeness Theorem 1.1. On consequences and
LOGIC I 1. The Completeness Theorem 1.1. On consequences and

Topic 1: Combinatorics & Probability
Topic 1: Combinatorics & Probability

Logarithm
Logarithm

Grade 6 Alternate Eligible Math Content
Grade 6 Alternate Eligible Math Content

looking at graphs through infinitesimal microscopes
looking at graphs through infinitesimal microscopes

More properties in Goldbach`s Conjecture
More properties in Goldbach`s Conjecture

THE DEVELOPMENT OF THE PRINCIPAL GENUS
THE DEVELOPMENT OF THE PRINCIPAL GENUS

Proof Search in Modal Logic
Proof Search in Modal Logic

< 1 ... 19 20 21 22 23 24 25 26 27 ... 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