• 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
PDF
PDF

Math Voc. - knomi.net
Math Voc. - knomi.net

... • A number that cannot be expressed as a ratio between two integers and is not an imaginary number. If written in decimal notation, an irrational number would have an infinite number of digits to the right of the decimal point, without repetition. Pi and the square root of 2 (2) are irrational numbe ...
Math 3345-Real Analysis — Lecture 01 8/31/05 1. What`s Real
Math 3345-Real Analysis — Lecture 01 8/31/05 1. What`s Real

Rational Numbers and Operations
Rational Numbers and Operations

... Mathematical Definition: A rational number is any number that can be written in the m form where m and n are both integers but n cannot be zero. n Set builder notation: Q = ...
Numbers, proof and `all that jazz`.
Numbers, proof and `all that jazz`.

Prime v Composite numbers
Prime v Composite numbers

2015 High School Math Contest - Wisconsin Mathematics Council
2015 High School Math Contest - Wisconsin Mathematics Council

Agebra 1 CCSS Math Chapter 1 alignment
Agebra 1 CCSS Math Chapter 1 alignment

... A-SSE.3c: Use the properties of exponents to transform expressions for exponential functions ...
Prolog arithmetic
Prolog arithmetic

Meraresult.com
Meraresult.com

Philosophy as Logical Analysis of Science: Carnap, Schlick, Gödel
Philosophy as Logical Analysis of Science: Carnap, Schlick, Gödel

Lecture 6: End and cofinal extensions
Lecture 6: End and cofinal extensions

Counting and Cardinality Operations and Algebraic Thinking
Counting and Cardinality Operations and Algebraic Thinking

A Short Glossary of Metaphysics
A Short Glossary of Metaphysics

Grade 3 PowerPoint
Grade 3 PowerPoint

Sequent calculus - Wikipedia, the free encyclopedia
Sequent calculus - Wikipedia, the free encyclopedia

Functions, Grade 11, University/College Preparation (MCF3M)
Functions, Grade 11, University/College Preparation (MCF3M)

Homework and Pre-Class reading for Math 152H
Homework and Pre-Class reading for Math 152H

Year 2 The principal focus of mathematics teaching in lower key
Year 2 The principal focus of mathematics teaching in lower key

Middle School Mathematics Pre-Test Sample Questions
Middle School Mathematics Pre-Test Sample Questions

Question 1. a) Prove that √ 10 is irrational. Solution: assume √ 10
Question 1. a) Prove that √ 10 is irrational. Solution: assume √ 10

Rational Numbers
Rational Numbers

Discrete mathematics I. practice
Discrete mathematics I. practice

MATH 1200: Tutorial 5, July 14 and July 21 Factorization is Not
MATH 1200: Tutorial 5, July 14 and July 21 Factorization is Not

... Inagine yourself in a world (referred to as the E-Zone) where the only numbers that are known are the even numbers. So, in this world, the only numbers that exist are E = {. . . , −8, −6, −4, −2, 0, 2, 4, 8, 10, . . .} . Notice that in the E-zone we can add, subtract, and multiply numbers just as us ...
majlis peperiksaan malaysia
majlis peperiksaan malaysia

< 1 ... 144 145 146 147 148 149 150 151 152 ... 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