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'''Logical equality''' is an operation on two logical values, typically the values of two propo |+ style="height:30px" | <math>\text{Logical Equality}\!</math>

...rix affords a matrix representation of a <math>k\!</math>-adic [[relation (mathematics)|relation]]. * [[Logical equality]]

...lational constructibility''' have to do with the ways that one [[relation (mathematics)|relation]] is determined by an indexed family or a sequence of other relat * [[Logical equality]]

* [[Logical equality]] [[Category:Discrete mathematics]]

A '''finitary boolean function''' is a [[function (mathematics)|function]] of the form <math>f : \mathbb{B}^k \to \mathbb{B},</math> where * [[Logical equality]]

* [[Logical equality]] * [[Relation (mathematics)|Relation]]

* [[Logical equality]] * [[Relation (mathematics)|Relation]]

* [[Logical equality]] * [[Relation (mathematics)|Relation]]

* [[Logical equality]] * [[Relation (mathematics)|Relation]]

==Logical equality== '''[[Logical equality]]''' is an operation on two logical values, typically the values of two pro

* [[Logical equality]] * [[Relation (mathematics)|Relation]]

* [[Logical equality]] * [[Relation (mathematics)|Relation]]

In the formal sciences &mdash; mathematics, mathematical logic, statistics &mdash; and their applied disciplines, a bo * Mathematical Society of Japan, ''Encyclopedic Dictionary of Mathematics'', 2nd edition, 2 vols., Kiyosi Itô (ed.), MIT Press, Cambridge, MA, 1993.

* [[Logical equality]] * [[Relation (mathematics)|Relation]]

* [[Logical equality]] * [[Relation (mathematics)|Relation]]

* [[Logical equality]] * [[Relation (mathematics)|Relation]]

* [[Logical equality]] * [[Relation (mathematics)|Relation]]

* [[Logical equality]] * [[Relation (mathematics)|Relation]]

* [[Logical equality]] * [[Relation (mathematics)|Relation]]

* [[Logical equality]] * [[Relation (mathematics)|Relation]]

* [[Logical equality]] * [[Relation (mathematics)|Relation]]

...precisely, the '''logic of relative terms''', is the study of [[relation (mathematics)|relation]]s as represented in symbolic forms known as ''rhemes'', ''rhemat ...ion Algebras'', vol. 150 in &lsquo;Studies in Logic and the Foundations of Mathematics&rsquo;, Elsevier Science, 2006.

* [[Logical equality]] * [[Relation (mathematics)|Relation]]

...ntroduced [[Charles Sanders Peirce]] (CP&nbsp;4.235, &ldquo;[[The Simplest Mathematics]]&rdquo; (1902), in ''Collected Papers'', CP&nbsp;4.227&ndash;323). * [[Logical equality]]

..., as described by Charles Sanders Peirce, is a special type of [[relation (mathematics)|relational predicate]] that arises as the limit of an iterated process of * [[Logical equality]]

* [[Logical equality]] * [[Relation (mathematics)|Relation]]

[[Graph (mathematics)]] [[Logical equality]]

* [[Logical equality]] * [[Relation (mathematics)|Relation]]

[[Graph (mathematics)]] [[Logical equality]]

* Peirce, C.S. (1902), &ldquo;The Simplest Mathematics&rdquo;. First published as CP&nbsp;4.227&ndash;323 in ''Collected Papers'' * [[Logical equality]]

* [[Logical equality]] * [[Relation (mathematics)|Relation]]

...ogical [[function (mathematics)|function]], a specific logical [[relation (mathematics)|relation]], and the various symbols that are used to denote this function ...ion while the implication is the ''asserted'' relation. In most fields of mathematics, it is treated as a variation in the usage of the single sign <math>{}^{\ba

...lize the concept of a [[binary relation]], such as the binary relations of equality and order that are denoted by the signs "=" and "<" in statements of the fo ...lize the concept of a [[binary relation]], such as the binary relations of equality and order that are denoted by the signs "=" and "<" in statements of the fo

In mathematics, a '''finitary relation''' is defined by one of the formal definitions give ...generalize the concept of a two-place relation, such as the relation of ''equality'' denoted by the sign &ldquo;<math>=\!</math>&rdquo; in a statement like <m

...gic : A Contribution to the Philosophy of Notation", ''American Journal of Mathematics'' 7 (1885), 180&ndash;202. Reprinted (CP&nbsp;3.359&ndash;403), (CE&nbsp;5 * [[Logical equality]]

* [[Logical equality]] * [[Relation (mathematics)|Relation]]

...h.edu/~bhl/bhl/BentleyMap/HTML/Images/JPEG/angellhall3.jpg Graduate Study, Mathematics], [http://www.umich.edu/ University of Michigan]. ...[http://www.uiuc.edu/navigation/buildings/altgeld.top.html Graduate Study, Mathematics], [http://www.uiuc.edu/ University of Illinois] at Urbana–Champaign.

...al reducibility''' have to do with the extent to which a given [[relation (mathematics)|relation]] is determined by a set of other relations, called the ''relatio * [[Logical equality]]

...oint of <math>\mathbb{B}^k~\!</math> is the unique point in the ''[[fiber (mathematics)|fiber]] of truth'' <math>[|s|]~\!</math> of a ''singular proposition'' <ma : In mathematics generally, the ''[[fiber (mathematics)|fiber]]'' of a point <math>y \in Y~\!</math> under a function <math>f : X

* [[Logical equality]] * [[Relation (mathematics)|Relation]]

* [[Logical equality]] * [[Relation (mathematics)|Relation]]

...spective of combinatorics, in other words, as a subject matter in discrete mathematics, with special attention to finite structures and concrete set-theoretic con ...lation has been developed quite literally from the beginnings of logic and mathematics, and because it has incorporated contributions from a diversity of thinkers

...lize the concept of a [[binary relation]], such as the binary relations of equality and order that are denoted by the signs "=" and "<" in statements of the fo ...lize the concept of a [[binary relation]], such as the binary relations of equality and order that are denoted by the signs "=" and "<" in statements of the fo

* [[Logical equality]] * [[Relation (mathematics)|Relation]]

'''Relation composition''', or the composition of [[relation (mathematics)|relations]], is the generalization of function composition, or the composi The first order of business is to define the operation on [[relation (mathematics)|relations]] that is variously known as the ''composition of relations'', '

...s that use the $ symbol). The U.S. dollar is divided into 100 ([[Equality (mathematics)|equal]]) [[cent (currency)|cent]]s. The U.S. dollar uses the decimal system, consisting of 100 ([[Equality (mathematics)|equal]]) cents (symbol ¢). In another division, there are 1,000 ''[[mill

====Operator Maps for the Logical Equality ''f''₉(u, v)==== =====Computation Summary for Equality=====

usually come up in mathematics, namely, in relation to the problem mathematics. In this discussion, I will invoke its application

...tand what a triadic relation is we need to understand what a ''[[relation (mathematics)|relation]]'' is, and here there are traditionally two ways of understandin * [[Logical equality]]

...ve just provided. Although equational forms of reasoning are paramount in mathematics, they are less familiar to the student of conventional logic textbooks, who ...A Contribution to the Philosophy of Notation&rdquo;, ''American Journal of Mathematics'' 7 (1885), 180&ndash;202. Reprinted as CP&nbsp;3.359&ndash;403 and CE&nbs

...ve just provided. Although equational forms of reasoning are paramount in mathematics, they are less familiar to the student of conventional logic textbooks, who ...gic : A Contribution to the Philosophy of Notation", ''American Journal of Mathematics'' 7 (1885), 180–202. Reprinted as CP 3.359–403 and CE 5, 162–190.

...particular conception of truth, such as those used in art, ethics, logic, mathematics, philosophy, the sciences, or any discussion that either mentions or makes ...er'', or a ''language'' to which the representation bears some [[relation (mathematics)|relation]].

* [[Logical equality]] * [[Relation (mathematics)|Relation]]

...er'', or a ''language'' to which the representation bears some [[relation (mathematics)|relation]]. * [[Logical equality]]

...n, [http://www.math.uic.edu/~kauffman/Arithmetic.htm Box Algebra, Boundary Mathematics, Logic, and Laws of Form]. ...le, simulation, and so on forms an extremely important complex of ideas in mathematics, there being recognized under the generic idea of ''structure-preserving ma

===The Signs of Inclusion, Equality, Etc.=== <p>I shall follow Boole in taking the sign of equality to signify identity. Thus, if <math>\mathrm{v}\!</math> denotes the Vice-P

| Precept L_2. Equality. The Following Are Equivalent: | There are a number of standard ways in mathematics and statistics for talking about the subset <math>W\!</math> of the functio

...consider it a good thing to always know what we are talking about. Where mathematics encourages tolerance for uninterpreted symbols as intermediate terms, logic ...ble because, once they are set up, all the well-worked theory of numerical mathematics lies ready at hand as a tool for our further reasoning.

[[WP:3RR|Three revert rule]] violation on {{Article|Philosophy of mathematics}}. {{3RRV|Jon_Awbrey}}: <!-- USE UNDERSCORE INSTEAD OF SPACE! --> ...athematics&action=history] made on [[June 12]] [[2006]] to [[Philosophy of mathematics]]'''

...consider it a good thing to always know what we are talking about. Where mathematics encourages tolerance for uninterpreted symbols as intermediate terms, logic ...ble because, once they are set up, all the well-worked theory of numerical mathematics lies ready at hand as a tool for our further reasoning.

...consider it a good thing to always know what we are talking about. Where mathematics encourages tolerance for uninterpreted symbols as intermediate terms, logic ...ble because, once they are set up, all the well-worked theory of numerical mathematics lies ready at hand as a tool for our further reasoning.

...consider it a good thing to always know what we are talking about. Where mathematics encourages tolerance for uninterpreted symbols as intermediate terms, logic ...ble because, once they are set up, all the well-worked theory of numerical mathematics lies ready at hand as a tool for our further reasoning.

| occur throughout mathematics. | one always has the equality:

...the derivatives and the differentials of any functions usually come up in mathematics, namely, in relation to the problem of computing "locally linear approximat ...lexibility of this order is very useful, and it is quite common throughout mathematics. In this discussion, I will invoke its application under the name of the '

* [[Logical equality]] * [[Relation (mathematics)|Relation]]

known in mathematics as "representation principles". As it turns out, In Peirce's time, and even in some circles of mathematics today,

: NEM n, m = ''The New Elements of Mathematics by Charles S. Peirce'', vol. n, page m. * Peirce, C.S, ''The New Elements of Mathematics by Charles S. Peirce'', 4 volumes in 5, Carolyn Eisele (ed.), Mouton Publis

| NEM 4 = 'The New Elements of Mathematics', Vol. 4, Among other things, this gives the following notational equality:

...1762. At William & Mary, he enrolled in the philosophy school and studied mathematics, [[metaphysics]], and philosophy under Professor [[William Small]], who int Jefferson's commitment to equality was expressed in his successful efforts to abolish primogeniture in Virgini

2. Rubric of Universal Equality (RUE): X = P_j = Q_j for all j in J. is required by the RUI, and to assume without loss of generality the equality

...ons so functional as indicators of sets and so essential for examining the equality of sets that they can constitute a veritable criterion for the practical co [[Category:Mathematics]]

...blems of logic, that of producing a method for the discovery of methods in mathematics.</p> <i>American Journal of Mathematics</i>, 7(2), 180&ndash;202, (1885).</p>