• 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
G7-M2 Lesson 4 - Teacher
G7-M2 Lesson 4 - Teacher

... What do you think the rules would be for subtracting numbers with same sign? (Do not spend too much time on this question. Allow students to verbally experiment with their responses.) ...
Fibonacci Identities as Binomial Sums
Fibonacci Identities as Binomial Sums

Linear Contextual Modal Type Theory
Linear Contextual Modal Type Theory

Introduction to Logic
Introduction to Logic

How To Write Proofs Part I: The Mechanics of Proofs
How To Write Proofs Part I: The Mechanics of Proofs

Arithmetic Operations Revisited
Arithmetic Operations Revisited

Document
Document

5.1.1 Integers - OpenTextBookStore
5.1.1 Integers - OpenTextBookStore

Math 1 Support - Coweta County Schools
Math 1 Support - Coweta County Schools

Full text
Full text

... which is a contradiction, since/? as a divisor of 5 would divide the left-hand side of (12), contrary to the fact that/? is distinct from q, Pi,--,pm. Next, suppose that q\(a-2k -B) or that q\(a + 2k -B). Equation (12) clearly implies in such a case, a = B = l (mod /?). Also if q\a-2k°B^ we must hav ...
Formal Foundations of Computer Security
Formal Foundations of Computer Security

On Stern╎s Diatomic Sequence 0,1,1,2,1,3,2,3,1,4
On Stern╎s Diatomic Sequence 0,1,1,2,1,3,2,3,1,4

... Stern’s diatomic sequence is a simply defined sequence with an amazing set of properties. Our goal is to present many of these properties—those that have most impressed the author. The diatomic sequence has a long history; perhaps first appearing in print in 1858 [28], it has been the subject of sev ...
Curriculum Guide (L2)
Curriculum Guide (L2)

... Develop self reliance and team spirit. ...
Higher Order Logic - Indiana University
Higher Order Logic - Indiana University

Higher Order Logic - Theory and Logic Group
Higher Order Logic - Theory and Logic Group

Full text
Full text

... as a sum of non-consecutive Fibonacci numbers Fn , with initial terms F1 = 1, F2 = 2. We consider the distribution of the number of summands involved in such decompositions. Previous work proved that as n → ∞ the distribution of the number of summands in the Zeckendorf decompositions of m ∈ [Fn , Fn ...
Belief Revision in non
Belief Revision in non

Rational Expressions and Replacements
Rational Expressions and Replacements

Between Truth and Falsity
Between Truth and Falsity

... formulas will have 3n lines. It’s worth doing, maybe one. Exercise: Use a truth table to show that (p v q) ↔ (p →q) is not a tautology, but that the formulas are both weakly ...
Lesson 10: Writing and Expanding Multiplication Expressions
Lesson 10: Writing and Expanding Multiplication Expressions

... numbers in a term together is called the coefficient of the term.  After the word “term” is defined, students can be  shown what it means to “collect like terms” using the distributive property.  Expressions in expanded form are analogous to polynomial expressions that are written as a sum of monomi ...
Numeracy - Parent Workshop
Numeracy - Parent Workshop

... I can round decimals to the nearest decimal place. I can recognise and use number patterns and relationships, I can reduce a fraction to its simplest form. I can order fractions and decimals. I understand simple ratio. I can find a simple fraction or percentage of a number or amount. I can + and – n ...
Exceptional real Lucas sequences
Exceptional real Lucas sequences

RATIONAL NUMBERS
RATIONAL NUMBERS

Rational and Irrational Numbers
Rational and Irrational Numbers

Introduction to Logic
Introduction to Logic

< 1 ... 33 34 35 36 37 38 39 40 41 ... 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