relation - Article Index

Encyclopedia - Collatz Conjecture: Encyclopedia Ii - Collatz Conjecture - Other Ways Of Looking At It
Collatz conjecture - In reverse. There is another approach to prove the following conjecture, which considers the bottom-up method of g...   » Read the article

Encyclopedia - Bundle Theory: Encyclopedia - Bundle Theory
Bundle theory is the ontological theory about objecthood in which an object consists only of a collection (bundle) of properties. Accordi...   » Read the article

Encyclopedia - Binary Relation: Encyclopedia - Binary Relation
In mathematics, a binary relation, sometimes called dyadic relation, is a relation between two entities. It is exemplified by such ideas ...   » Read the article

Encyclopedia - Analogy: Encyclopedia - Analogy
Analogy is either the cognitive process of transferring information from a particular subject (the analogue or source) to another particu...   » Read the article

Encyclopedia - Abstraction: Encyclopedia - Abstraction
An abstraction is an idea, concept, or word which defines the phenomena that make up its referents (those concrete events or things to wh...   » Read the article

Encyclopedia - Category Of Being: Encyclopedia - Category Of Being
In metaphysics (in particular, ontology), the different kinds or ways of being are called categories of being or simply categories. Accor...   » Read the article

Encyclopedia - Axiomatic Set Theory: Encyclopedia - Axiomatic Set Theory
Set theory is a branch of mathematics created principally by the German mathematician Georg Cantor at the end of the 19th century. Initia...   » Read the article

Encyclopedia - Charles Peirce: Encyclopedia - Charles Peirce
Charles Sanders Santiago Peirce (pronounced purse), (September 10, 1839, Cambridge, Massachusetts – April 19, 1914, Milford, Pennsylvan...   » Read the article

Encyclopedia - Unity Of The Proposition: Encyclopedia - Unity Of The Proposition
In philosophy, the unity of the proposition is the problem of explaining how a sentence in the indicative mood expresses more than just w...   » Read the article

Encyclopedia - Cyclic Order: Encyclopedia - Cyclic Order
In combinatorial mathematics, a cyclic order on a set X with n elements is an arrangement of X as on a clock face, for an n-hour clock. T...   » Read the article

Encyclopedia - Correspondence Theory Of Truth: Encyclopedia - Correspondence Theory Of Truth
The correspondence theory of truth states that something is rendered true by the existence of a fact with corresponding elements and a si...   » Read the article

Encyclopedia - Well-defined: Encyclopedia - Well-defined
In mathematics, the term well-defined is used to specify that a certain concept (a function, a property, a relation, etc.) is defined in ...   » Read the article

Encyclopedia - String Computer Science: Encyclopedia - String Computer Science
In computer programming and some branches of mathematics, strings are sequences of various simple objects. These simple objects are selec...   » Read the article

Encyclopedia - Collatz Conjecture: Encyclopedia - Collatz Conjecture
The Collatz conjecture is an unresolved conjecture in mathematics. It is named after Lothar Collatz, who first proposed it in 1937. The c...   » Read the article

Encyclopedia - Experiment: Encyclopedia - Experiment
In the scientific method, an experiment is a set of actions and observations, performed to support or falsify a hypothesis or research co...   » Read the article

Encyclopedia - Nominalism: Encyclopedia - Nominalism
Nominalism is the position in metaphysics that there exist no universals outside of the mind. Nominalism is best understood in contrast t...   » Read the article

Encyclopedia - Behavior: Encyclopedia - Behavior
Behavior (or behaviour) refers to the actions or reactions of an object or organism, usually in relation to the environment. Behavior can...   » Read the article

Encyclopedia - Nominalism: Encyclopedia Ii - Nominalism - The Problem Of Universals
Nominalism arose in reaction to the problem of universals. Specifically, accounting for the fact that some things are of the same type. F...   » Read the article

Encyclopedia - Analogy: Encyclopedia Ii - Analogy - Models And Theories Of Analogy
Analogy - Identity of relation. In ancient Greek the word αναλογια (analogia) originally meant proportionality, in the mathemat...   » Read the article

Encyclopedia - Unity Of The Proposition: Encyclopedia Ii - Unity Of The Proposition - Russell Frege Wittgenstein
The problem became significant in the early development of set theory. Set membership is a formal representation of the relation between ...   » Read the article

Encyclopedia - Partial Function: Encyclopedia Ii - Partial Function - Discussion And Examples
The above diagram represents a partial function that is not a total function since the element 1 in X is not associated with anything. U...   » Read the article

Encyclopedia - Transfinite Induction: Encyclopedia Ii - Transfinite Induction - Relationship To Ac
There is a popular misconception that transfinite induction, or transfinite recursion, or both, require the axiom of choice (AC). This is...   » Read the article

Encyclopedia - Axiomatic Set Theory: Encyclopedia Ii - Axiomatic Set Theory - The Origins Of Rigorous Set Theory
The important idea of Cantor's, which got set theory going as a new field of study, was to define two sets A and B to have the same numbe...   » Read the article

Encyclopedia - Subset: Encyclopedia Ii - Subset - Properties
PROPOSITION 1: The empty set is a subset of every set. Proof: Given any set A, we wish to prove that ø is a subset of A. This involves s...   » Read the article

Encyclopedia - Function Mathematics: Encyclopedia Ii - Function Mathematics - Introduction
The modern idea of a mathematical function was introduced by Leibniz, and the associated notation y = f(x) was invented by Leonhard Euler...   » Read the article

Encyclopedia - Identity Philosophy: Encyclopedia Ii - Identity Philosophy - Metaphysics Of Identity
Metaphysicians, and sometimes philosophers of language and mind, ask other questions: What does it mean for an object to be the same as ...   » Read the article

Encyclopedia - Graph Of A Function: Encyclopedia Ii - Graph Of A Function - Tools For Plotting Function Graphs
Graph of a function - Hardware. Graphing calculator Oscilloscope Graph of a function - Software. See List of graphing software .....   » Read the article

Encyclopedia - Order Theory: Encyclopedia Ii - Order Theory - Introduction To The Basic Definitions
This section aims at giving a first guide to the realm of ordered sets. It addresses readers who have basic knowledge of set theory and a...   » Read the article

Encyclopedia - Patience Sorting: Encyclopedia Ii - Patience Sorting - Algorithm For Sorting
Given an n-element array with an ordering relation as an input for the sorting, consider it as a collection of cards, with the (unknown i...   » Read the article

Encyclopedia - Projective Space: Encyclopedia Ii - Projective Space - Morphisms
Projective linear maps between two projective spaces over the same field, say, P(V) and P(W), have the form where T is an element of L...   » Read the article

Encyclopedia - Political Argument: Encyclopedia Ii - Political Argument - Purpose Of Political Argument
The purpose of argument is usually to sway belief. Political argument can occur in the context of political theory; for instance Machiave...   » Read the article

Encyclopedia - Table Database: Encyclopedia Ii - Table Database - Tables Versus Relations
In terms of the relational model of databases, a table can be considered a convenient representation of a relation, but the two are not i...   » Read the article

Encyclopedia - Relational Model: Encyclopedia Ii - Relational Model - Set Theory Formulation
Basic notions in the relational model are relation names and attribute names. We will represent these as strings such as "Person" and "na...   » Read the article

Encyclopedia - Many-one Reduction: Encyclopedia Ii - Many-one Reduction - Definitions
Many-one reduction - Formal languages. Suppose A and B are formal languages over the alphabets Σ and Γ, respectively. A many-one redu...   » Read the article

Encyclopedia - Linear Temporal Logic: Encyclopedia Ii - Linear Temporal Logic - Syntax
LTL is built up from a set of proposition variables p1,p2,..., the usual logic connectives and the following temporal modal operators: ...   » Read the article

Encyclopedia - Institution Computer Science: Encyclopedia Ii - Institution Computer Science - Definition
An institution consists of a category Sign of signatures, a functor Set giving, for each signature Σ, the set of sentences sen(Σ), and...   » Read the article

Encyclopedia - Category Of Being: Encyclopedia Ii - Category Of Being - Categories Of Being
Philosophers have many differing views on what the fundamental categories of being are. In no particular order, here are at least some it...   » Read the article

Encyclopedia - Query Optimizer: Encyclopedia Ii - Query Optimizer - Implementation
Most query optimizers represent query plans as a tree of "plan nodes". A plan node encapsulates a single operation that is required to ex...   » Read the article

Encyclopedia - Tuple Relational Calculus: Encyclopedia Ii - Tuple Relational Calculus - Definition Of The Calculus
Tuple relational calculus - Relational database. Since the calculus is a query language for relational databases we first have to defin...   » Read the article

Encyclopedia - Subset: Encyclopedia Ii - Subset - Properties
PROPOSITION 1: The empty set is a subset of every set. Proof: Given any set A, we wish to prove that ø is a subset of A. This involves s...   » Read the article

Encyclopedia - Sign Relation: Encyclopedia Ii - Sign Relation - Six Ways Of Looking At A Sign Relation
Sign relation - IOS. (Text in preparation, 30 January 2006) Sign relation - ISO. (Text in preparation, 30 January 2006) Sign relatio...   » Read the article

Encyclopedia - Inequation: Encyclopedia Ii - Inequation - Properties
Some useful properties of inequations in algebra are: Any quantity can be added to both sides. Any quantity can be subtracted from both ...   » Read the article

Encyclopedia - Function Mathematics: Encyclopedia Ii - Function Mathematics - The Vocabulary Of Functions
An input to a function is called argument of the function. For each argument x, the corresponding unique y in the codomain is called the ...   » Read the article

Encyclopedia - Charles Peirce: Encyclopedia Ii - Charles Peirce - Peirce's Philosophy
It is not sufficiently recognized that Peirce’s career was that of a scientist, not a philosopher; and that during his lifetime he was ...   » Read the article

Encyclopedia - Function Mathematics: Encyclopedia Ii - Function Mathematics - Mathematical Definition Of A Function
A precise definition is required for the purposes of mathematics. A function is a binary relation, f, with the property that for an eleme...   » Read the article

Encyclopedia - Axiom Schema Of Replacement: Encyclopedia Ii - Axiom Schema Of Replacement - Statement
Suppose P is any predicate in two variables that doesn't use the symbol B. Then in the formal language of the Zermelo-Fraenkel axioms, th...   » Read the article

Encyclopedia - Bundle Theory: Encyclopedia Ii - Bundle Theory - Objections To The Bundle Theory
Objections to bundle theory concern the nature of the bundle of properties, the properties' compresence relation (the togetherness relati...   » Read the article

Encyclopedia - Determinacy: Encyclopedia Ii - Determinacy - Basic Notions
Determinacy - Games. The first sort of game we shall consider is the two-player game of perfect information of length ω, in which the ...   » Read the article

Encyclopedia - Forcing Mathematics: Encyclopedia Ii - Forcing Mathematics - The Countable Chain Condition
An antichain A of P is a subset such that if p and q are in A, then p and q are incompatible (written p ⊥ q), meaning there is no r in ...   » Read the article

Encyclopedia - String Computer Science: Encyclopedia Ii - String Computer Science - String Datatypes
A string datatype is a datatype modeled on the idea of a formal string. Strings are such an important and useful datatype that they are i...   » Read the article

Encyclopedia - Abstraction: Encyclopedia Ii - Abstraction - Referents
Abstractions sometimes have ambiguous referents; for example, "happiness" (when used as an abstraction) can refer to many things as there...   » Read the article

Encyclopedia - Category Of Being: Encyclopedia Ii - Category Of Being - Categories Of Being
Philosophers have many differing views on what the fundamental categories of being are. In no particular order, here are at least some it...   » Read the article

Encyclopedia - Charles Peirce: Encyclopedia Ii - Charles Peirce - Peirce's Philosophy
It is not sufficiently recognized that Peirce’s career was that of a scientist, not a philosopher; and that during his lifetime he was ...   » Read the article

Encyclopedia - Experiment: Encyclopedia Ii - Experiment - Controlled Experiments
Many hypotheses in sciences such as physics can establish causality by noting that, until some phenomenon occurs, nothing happens; then w...   » Read the article

Encyclopedia - Binary Relation: Encyclopedia Ii - Binary Relation - Relations Over A Set
If X = Y then we simply say that the binary relation is over X. Or it is an endorelation over X. Some important classes of binary relatio...   » Read the article

Encyclopedia - Proportionality Mathematics: Encyclopedia Ii - Proportionality Mathematics - Inverse Proportionality
As noted in the definition above two proportional variables are sometime said to be directly proportional. This is done so as to contrast...   » Read the article

Encyclopedia - String Computer Science: Encyclopedia Ii - String Computer Science - String Datatypes
A string datatype is a datatype modeled on the idea of a formal string. Strings are such an important and useful datatype that they are i...   » Read the article

Encyclopedia - Bundle Theory: Encyclopedia Ii - Bundle Theory - Objections To The Bundle Theory
Objections to bundle theory concern the nature of the bundle of properties, the properties' compresence relation (the togetherness relati...   » Read the article

Encyclopedia - Collatz Conjecture: Encyclopedia Ii - Collatz Conjecture - Examples
For instance, starting with n = 6, one gets the sequence 6, 3, 10, 5, 16, 8, 4, 2, 1. (The Collatz conjecture says that this process alwa...   » Read the article

Article - Popular Topic Pages Ii - 18
This is a sitemap for popular topic pages at Global Oneness. Click on a link and you will find multiple articles related to the topic: ...   » Read the article

Encyclopedia - Collatz Conjecture: Encyclopedia Ii - Collatz Conjecture - Program To Calculate Collatz Sequences
A specific Collatz sequence can be easily computed, as is shown by this pseudocode example: def collatz(n) show n if n.odd? and n &g...   » Read the article

Article - Popular Topic Pages Ii - 26
This is a sitemap for popular topic pages at Global Oneness. Click on a link and you will find multiple articles related to the topic: ...   » Read the article

Encyclopedia - Collatz Conjecture: Encyclopedia Ii - Collatz Conjecture - Statement Of The Problem
Consider the following operation on an arbitrary positive integer: If the number is even, divide it by two. If the number is odd, triple...   » Read the article

Encyclopedia - Bundle Theory: Encyclopedia Ii - Bundle Theory - Arguments For The Bundle Theory
The difficulty in conceiving of or describing an object without also conceiving of or describing its properties is a common justification...   » Read the article

Encyclopedia - String Computer Science: Encyclopedia Ii - String Computer Science - String Algorithms
There are many algorithms for processing strings, each with various tradeoffs. Some categories of algorithms include string searching al...   » Read the article

Encyclopedia - Charles Peirce: Encyclopedia Ii - Charles Peirce - Bibliography
Charles Peirce - Primary literature. Abbreviations for frequently cited works: CE n, m = Writings of Charles S. Peirce: A Chronologica...   » Read the article

Encyclopedia - String Computer Science: Encyclopedia Ii - String Computer Science - String Oriented Languages And Utilities
Strings are such a useful datatype that several languages have been designed in order to make string processing applications easy to writ...   » Read the article

Encyclopedia - Charles Peirce: Encyclopedia Ii - Charles Peirce - Works
Peirce's reputation is based in large part on a number of academic papers published in American scholarly and scientific journals. These ...   » Read the article

Encyclopedia - Bundle Theory: Encyclopedia Ii - Bundle Theory - Bundle Theory And Eastern Philosophy
Candrakirti, the famous Madhyamaka philosopher used the aggregate nature of objects to demonstrate the lack of essence in what is known a...   » Read the article

Encyclopedia - Function Mathematics: Encyclopedia Ii - Function Mathematics - Domain Codomain Argument Image
If f is a function from X to Y, the set X is called the domain of f, and Y is called its codomain. Each element of the domain is called a...   » Read the article

Encyclopedia - Determinacy: Encyclopedia Ii - Determinacy - Consequences Of Determinacy
Determinacy - Regularity properties for sets of reals. If A is a subset of Baire space such that the Banach-Mazur game for A is determi...   » Read the article

Encyclopedia - Function Mathematics: Encyclopedia Ii - Function Mathematics - Functions In Other Fields
Functions are used in every quantitative science, to model relationships between all kinds of physical quantities — especially when one...   » Read the article

Encyclopedia - Determinacy: Encyclopedia Ii - Determinacy - Determinacy And Large Cardinals
There is an intimate relationship between determinacy and large cardinals. In general, stronger large cardinal axioms prove the determina...   » Read the article

Encyclopedia - Determinacy: Encyclopedia Ii - Determinacy - Determinacy From Zfc
In 1975, Donald A. Martin proved that all Borel games are determined; that is, if A is a Borel subset of Baire space, then GA is determin...   » Read the article

Encyclopedia - Determinacy: Encyclopedia Ii - Determinacy - Determinacy From Elementary Considerations
Familiar real-world games of perfect information, such as chess or tic-tac-toe, are always finished in a finite number of moves. (It is a...   » Read the article

Encyclopedia - Charles Peirce: Encyclopedia Ii - Charles Peirce - Reception
Bertrand Russell opined, "Beyond doubt … he was one of the most original minds of the later nineteenth century, and certainly the great...   » Read the article

Encyclopedia - Charles Peirce: Encyclopedia Ii - Charles Peirce - Life
Right from the beginning, the relations of America as New England with Europe were, from the philosophical point of view, ambiguous, when...   » Read the article

Encyclopedia - Function Mathematics: Encyclopedia Ii - Function Mathematics - Classes Of Functions
Function mathematics - Injective surjective bijective. Three important properties that a function may have are: injective (or one-to-o...   » Read the article

Encyclopedia - Function Mathematics: Encyclopedia Ii - Function Mathematics - Restrictions And Extensions
Informally, a restriction of a function f is the result of trimming its graph to a smaller domain. More precisely, if f is a function fro...   » Read the article

Encyclopedia - Function Mathematics: Encyclopedia Ii - Function Mathematics - Composing Functions
The functions f: X → Y and g: Y → Z can be composed by first applying f to an argument x and then apply...   » Read the article

Encyclopedia - Function Mathematics: Encyclopedia Ii - Function Mathematics - Set Of All Functions
The set of all functions from a set X to a set Y is denoted by X → Y, by [X → Y], or by YX. The latter notation is justified by the f...   » Read the article

Encyclopedia - Function Mathematics: Encyclopedia Ii - Function Mathematics - Partial Functions And Multi-functions
The condition for a binary relation f from X to Y to be a function can be split into two conditions: f is total, or entire: for each x i...   » Read the article

Encyclopedia - Function Mathematics: Encyclopedia Ii - Function Mathematics - Image Of A Set
One often extends the concept (and notation) of image of an argument to sets of arguments. Namely, if A is any subset of the domain X, th...   » Read the article

Encyclopedia - Function Mathematics: Encyclopedia Ii - Function Mathematics - Pointwise Operations
If f: X → R and g: X → R are functions with common domain X and codomain is a ring R, then one can defi...   » Read the article

Encyclopedia - Function Mathematics: Encyclopedia Ii - Function Mathematics - Functions In Category Theory
The notion of function is generalizes to the notion of morphism in the context of category theory. A category is a collection of objects ...   » Read the article

Encyclopedia - Function Mathematics: Encyclopedia Ii - Function Mathematics - Graph Of A Function
The graph of a function f is the set of all ordered pairs (x, f(x)), for all x in the domain X. If X and Y are the set of real numbers (o...   » Read the article

Encyclopedia - Function Mathematics: Encyclopedia Ii - Function Mathematics - Specifying A Function
If the domain X is finite, a function f may be defined by simply tabulating all the arguments x and their corresponding function values f...   » Read the article

Encyclopedia - Function Mathematics: Encyclopedia Ii - Function Mathematics - Functions With Multiple Inputs And Outputs
Function mathematics - Functions of two or more variables. The concept of function can be extended to an object that takes a combinatio...   » Read the article

Encyclopedia - Function Mathematics: Encyclopedia Ii - Function Mathematics - Is A Function More Than Its Graph?
Most mathematicians define a binary relation (and hence a function) as an ordered triple (X, Y, G), where X and Y are the domain and codo...   » Read the article

Encyclopedia - String Computer Science: Encyclopedia Ii - String Computer Science - Character String Oriented Languages And Utilities
Character strings are such a useful datatype that several languages have been designed in order to make string processing applications ea...   » Read the article

Encyclopedia - Function Mathematics: Encyclopedia Ii - Function Mathematics - Restrictions And Extensions
Informally, a restriction of a function f is the result of trimming its graph to a smaller domain. More precisely, if f is a function fro...   » Read the article

Encyclopedia - Function Mathematics: Encyclopedia Ii - Function Mathematics - Pointwise Operations
If f: X → R and g: X → R are functions with common domain X and codomain is a ring R, then one can defi...   » Read the article

Encyclopedia - Function Mathematics: Encyclopedia Ii - Function Mathematics - Functions In Category Theory
The notion of function is generalizes to the notion of morphism in the context of category theory. A category is a collection of objects ...   » Read the article

Encyclopedia - Function Mathematics: Encyclopedia Ii - Function Mathematics - Partial Functions And Multi-functions
The condition for a binary relation f from X to Y to be a function can be split into two conditions: f is total, or entire: for each x i...   » Read the article

Encyclopedia - Function Mathematics: Encyclopedia Ii - Function Mathematics - Is A Function More Than Its Graph?
Most mathematicians define a binary relation (and hence a function) as an ordered triple (X, Y, G), where X and Y are the domain and codo...   » Read the article

Encyclopedia - Function Mathematics: Encyclopedia Ii - Function Mathematics - Functions With Multiple Inputs And Outputs
Function mathematics - Functions of two or more variables. The concept of function can be extended to an object that takes a combinatio...   » Read the article

Encyclopedia - Function Mathematics: Encyclopedia Ii - Function Mathematics - Set Of All Functions
The set of all functions from a set X to a set Y is denoted by X → Y, by [X → Y], or by YX. The latter notation is justified by the f...   » Read the article

Encyclopedia - Bundle Theory: Encyclopedia Ii - Bundle Theory - Bundle Theory And Eastern Philosophy
Candrakirti, the famous Madhyamaka philosopher used the aggregate nature of objects to demonstrate the lack of essence in what is known a...   » Read the article

Encyclopedia - Linear Temporal Logic: Encyclopedia Ii - Linear Temporal Logic - Semantics
An LTL formula can be evaluated over a sequence of truth evaluations and a position on that path. An LTL formula is satisfied by a path i...   » Read the article

Encyclopedia - Sign Relation: Encyclopedia Ii - Sign Relation - Bibliography
Sign relation - Primary Sources. Sign relation - Secondary Sorces. Deledalle, Gérard, 2000. C.S. Peirce's Philosophy of Signs. Indi...   » Read the article

Encyclopedia - Binary Relation: Encyclopedia Ii - Binary Relation - Special Types Of Relations
Some important classes of binary relations R over X and Y are: total: for all x in X there exists a y in Y such that xRy (this definitio...   » Read the article