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Topic: Equality (objects)

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Equality (mathematics) - Wikipedia, the free encyclopedia A stronger sense of equality is obtained if some form of Leibniz's law is added as an axiom; the assertion of this axiom rules out "bare particulars"—things that have all and only the same properties but are not equal to each other—which are possible in some logical formalisms. Given a set A, the restriction of equality to the set A is a binary relation, which is at once reflexive, symmetric, antisymmetric, and transitive. In mathematics, two mathematical objects are considered equal if they are precisely the same in every way. www.wikipedia.org /wiki/Equal+(math)   (620 words)

Eq Eqbal Ahmad Eqbal Ahmad Eqerem Spahia Equal Equal math Equal mathematics Equal maths Equality (mathematics) - In, two mathematical objects are considered equal... Equality of outcome - Equality of outcome is a basic form of... Equality (mathematics) - Given the definition of "antisymmetric" on the... www.geodatabase.de /?Eq   (860 words)

plato.html This "equality" is far from identity if the *symbols* are looked upon, for the ratio of a large circle to its diameter is expressed as C:D, while the "equal" ratio for a small circle might be expressed "c:d", quite a different set of symbols. I disputed this, and claimed that to these students equality was identity rather than approximation, something that seems to be troubling the schools these days in those places where the calculator is regarded as the repository of truth. Nothing we write on paper is a mathematical object; mathematical objects are ideals and dwell in Plato's heaven. www.math.rochester.edu /people/faculty/rarm/plato.html   (2608 words)

Problems with Relativity The argument for the equality of gravitational and inertial mass is thus shown to be untenable, and the Equivalence Principle is wrong. Einstein states that all objects when dropped, will fall to the floor with equal acceleration, whether the chest is in a gravitational field or is being accelerated by an outside force. This applies whatever the mass of the bodies, and explains why the wood and the lead appear to behave the same - their mass is so tiny compared to that of the Earth, that for all practical purposes when dealing with the Earth, they are identical in mass. members.aol.com /carmam1534/Hollings.html   (2608 words)

Blogger: Email Post to a Friend Rather, we are challenging our culture's peculiar and damaging definition of women's breasts as sex objects, which hinders breastfeeding, breast cancer detection, body acceptance, and treatment of women as equals. "The aim of the ["topfree"] picnic is not to fight the problem of ignorance of women's legal right to go topfree in New York State. their RIGHT) to go "topfree" in Dewitt Park is all anyone can talk about. www.blogger.com /email-post.g?blogID=2861218&postID=79357499   (216 words)

Smith Robertson Museum - "TESTIMONY" Testimony presents a range of arresting artworks, from large-scale paintings and reliefs, to small and lyrical works on paper, to complex, inventive assemblages of metal, wood, fiber, and found objects. Testimony is curated by Dr. Howard Dodson, Director of the Schomburg Center for Research in Black Culture of the New York Public Library. Testimony is an expanded, thematically organized exhibition based on an acclaimed show mounted by The Schomburg Center in 197 and seen only in New York. www.city.jackson.ms.us /CityHall/testimony%20exhibit%20(Smith%20Robertson).htm   (216 words)

Equality Through its connection with justice, equality, like justice itself, has different justitianda, i.e., objects the term ‘just’ or ‘equal’ or their opposites can be applied to. There is controversy concerning the precise notion of equality, the relation of justice and equality (the principles of equality), the material requirements and measure of the ideal of equality (equality of what?), the extension of equality (equality among whom?), and its status within a comprehensive (liberal) theory of justice (the value of equality). Equality is thus merely a byproduct of the general fulfillment of actually non-comparative standards of justice: something obscured through the unnecessary inserting of an expression of equality (Raz 1986, p. plato.stanford.edu /entries/equality   (13525 words)

Ontological Dependence Similarly, unless we are prepared to regard places as parts of the objects occupying them, or again to deny their existence altogether, we shall have to conclude that only unlocated mental entities—immaterial souls, perhaps—could qualify as substances. Notice, here, that we allow that x may be said to depend for its identity upon y even in cases in which the identity of y alone does not suffice to fix the identity of x. These relationships of identity-dependence are direct consequences of the identity-criteria governing the kinds of which the items thus related are instances. plato.stanford.edu /entries/dependence-ontological   (6513 words)

Equality (mathematics) - Wikipedia, the free encyclopedia Given a set A, the restriction of equality to the set A is a binary relation, which is at once reflexive, symmetric, antisymmetric, and transitive. This defines a binary predicate, equality, denoted "="; x = y iff x and y are equal. In mathematics, two mathematical objects are considered equal if they are precisely the same in every way. www.wikipedia.org /wiki/Substitution_property_of_equality   (679 words)

Equality (mathematics) - Wikipedia, the free encyclopedia Given a set A, the restriction of equality to the set A is a binary relation, which is at once reflexive, symmetric, antisymmetric, and transitive. This defines a binary predicate, equality, denoted "="; x = y iff x and y are equal. In mathematics, two mathematical objects are considered equal if they are precisely the same in every way. en.wikipedia.org /wiki/Equality_(mathematics)   (679 words)

Standards - Mathematics - Fifth Grade - USD 259 substitution property of equality [i.e.: (4 + 3) + 5 = 7 + 5 and a = 3, and a = b, then b = 3]. All students will understand, apply and analyze concepts of geometric shapes, spatial relationships, transformations, and real-life applications of geometry; understand measurable attributes of objects and the units, systems, and processes of measurement; and apply appropriate techniques, tools, and formulas to determine measurement. associative properties of + and × [i.e.: 4 + (2 + 3) = (4 + 2) + 3]. www.usd259.com /curriculum/standards/math-fifth.html   (1855 words)

Java vs. C# You should implement an Equals() method in C#, just like equals() in Java, but you should also overload the equality operator == to 'teach' your custom class to do the comparison of the contents of both objects with this operator. In Java, using the equality operator == to compare objects is a no-no. Instead, Java programmers train themselves to use equals() instead: Otherwise, programmers will try to use the == operator with your classes and get the (unexpected) Java effect of having objects never compare equally even though their contents are internally the same. www.extremetech.com /article2/0,1558,1164818,00.asp   (1425 words)

ACM OOPS Messenger 4, 4 (Oct 1993), 2-27 This model of object identity, which is analogous to the normal forms of relational algebra, provides cleaner semantics for the value-transmission operations and built-in primitive equality predicate of a programming language, and eliminates the confusion surrounding "call-by-value" and "call-by-reference" as well as the confusion of multiple equality predicates. The simplest treatment of object identity for abstract objects is to ignore the abstraction and use the object identity of the representation; this choice is the only one available to programmers in languages which do not support abstract data types. will distinguish between abstract objects which may be abstractly equivalent, but have different representations--perhaps as the result of a new implementation of the abstract type having been instantiated. home.pipeline.com /~hbaker1/ObjectIdentity.html   (15312 words)

David Hayden : Object Identity vs. Object Equality - Overriding System.Object.Equals(Object obj) In other words, equality may mean more about the objects having the same field values and not that they are the same instance. However, many times the test for equality between two objects is not about referential semantics, but value semantics. If the objects being compared are the same instance, they are considered equal. codebetter.com /blogs/david.hayden/archive/2005/02/22/51364.aspx   (1145 words)

equal. The American Heritage® Dictionary of the English Language: Fourth Edition. 2000. When someone says The two boards are of equal length, we assume that the equality is reckoned to some order of approximation determined by the context; if we did not, we would be required always to use nearly equal when speaking of the dimensions of physical objects. Objections to the more equal construction rest on the assumption that the mathematical notion of equality is appropriate to the description of a world where the equality of two quantities is often an approximate matter, and where statements of equality are always relative to an implicit standard of tolerance. What is more, we often speak of the equality of things that cannot be measured quantitatively, as when we say The college draft was introduced in an effort to make the teams in the National Football League as equal as possible, or The candidates for the job should all be given equal consideration. www.bartleby.com /61/70/E0187000.html   (545 words)

: Interface Comparator Tests equality of two objects in the universe over which this comparator is defined. A comparator does comparisons of objects in the universe the comparator is defined over. Tests strict order of two objects in the universe over which this comparator is defined. www.apl.jhu.edu /Classes/Notes/Johnson/605.202/jdsl/jdsl/Comparator.html   (264 words)

equal - yourDictionary.com - American Heritage Dictionary we assume that the equality is reckoned to some order of approximation determined by the context; if we did not, we would be required always to use nearly equal when speaking of the dimensions of physical objects. Objections to the more equal construction rest on the assumption that the mathematical notion of equality is appropriate to the description of a world where the equality of two quantities is often an approximate matter, and where statements of equality are always relative to an implicit standard of tolerance. To eliminate the redundancy, equally should be deleted from the first example and as from the second. www.yourdictionary.com /ahd/e/e0187000.html   (445 words)

Practical Foundations of Mathematics Whereas morphisms of a category are in some sense isolated from one another, functors (like the objects which are their values) have a kind of fluidity between them, given by the morphisms of the target category, which we haven't taken into account. The first task of category theory is an organisational one: after various kinds of objects (types, sets, posets, complete semilattices and dcpos) and maps (terms, relations; partial, total, monotone, continuous and structure- preserving functions; and adjunctions) have been introduced, we were able to put them in a common framework as categories. For the (large) category-domains mentioned above, it is still possible to control the size of the functor categories, because the functors in question are Scott-continuous and are therefore determined by their values on ``finite'' objects as in Proposition 3.4.12. www.cs.man.ac.uk /~pt/Practical_Foundations/html/s48.html   (1934 words)

Practical Foundations of Mathematics Equivalences Functors are the means of exchange between categories, so since functors are only defined up to isomorphism, exchange between categories is a notion of isomorphism that is further weakened by putting isomorphism for equality. Whereas morphisms of a category are in some sense isolated from one another, functors (like the objects which are their values) have a kind of fluidity between them, given by the morphisms of the target category, which we haven't taken into account. As we have said, mathematical constructions generally define objects only up to isomorphism, because frequently there is a different but equally useful representation which can be substituted. www.cs.man.ac.uk /~pt/Practical_Foundations/html/s48.html   (1934 words)

CLHS: Function EQUAL equal is true of two objects if they are symbols that are eq, if they are numbers that are eql, or if they are characters that are eql. Object equality is not a concept for which there is a uniquely determined correct algorithm. Any two objects that are eql are also equal. www.lispworks.com /documentation/HyperSpec/Body/f_equal.htm   (364 words)

Leggett: Democratick Editorials, Part IV, Essays 6-11: Library of Economics and Liberty Amongst leading articles there is one entitled Loco Focos, which professes to give an account of the principles and objects of the political party known by that name. It is not to be doubted that, with the mere exception of such a sprinkling as all parties contain of men governed by selfish motives, the Loco Focos are sincere in the creed and in the objects which they profess. The whole creed of those who are termed Loco Focos is embraced in the maxim of the equality of men's political rights. www.econlib.org /library/Leggett/lgtDE10.html   (364 words)

ACM OOPS Messenger 4, 4 (Oct 1993), 2-27 This model of object identity, which is analogous to the normal forms of relational algebra, provides cleaner semantics for the value-transmission operations and built-in primitive equality predicate of a programming language, and eliminates the confusion surrounding "call-by-value" and "call-by-reference" as well as the confusion of multiple equality predicates. Trivial mutable objects of this kind can be used for unforgeable keys, because the only way one could have gotten such a key is by communicating with some object which already had it, since the generator of such objects is guaranteed to produce a new, never-before-seen (modulo garbage collection) object. For example, an object with a functional attribute might represent the attribute directly if it is small and if it belongs to a type which can be represented in a number of bits which can be fixed at compile time; alternatively, it could represent the attribute through a pointer to another functional object. www.pipeline.com /~hbaker1/ObjectIdentity.html   (15312 words)

ACM OOPS Messenger 4, 4 (Oct 1993), 2-27 This model of object identity, which is analogous to the normal forms of relational algebra, provides cleaner semantics for the value-transmission operations and built-in primitive equality predicate of a programming language, and eliminates the confusion surrounding "call-by-value" and "call-by-reference" as well as the confusion of multiple equality predicates. If programming languages distinguish functional/immutable objects from non-functional/mutable objects, and if programs utilize a "mostly functional" style, then such programs will be efficient even in a non-shared-memory ("message-passing") implementation. The ability of a program in a language to call subprograms in other languages has become an feature essential to a programming language's ability to survive the recent "standardization craze". www.pipeline.com /~hbaker1/ObjectIdentity.html   (15312 words)

string (C# Programmer's Reference) Although string is a reference type, the equality operators (== and !=) are defined to compare the values of string objects, not references (7.9.7 String equality operators). string a = "hello"; string b = "h"; b += "ello"; // append to b Console.WriteLine(a == b); // output: True -- same value Console.WriteLine((object)a == b); // False -- different objects string is an alias for System.String in the.NET Framework. msdn.microsoft.com /library/en-us/csref/html/vclrfstring.asp   (15312 words)

Hashtable Class (.NET Framework) If key equality were simply reference equality, the inherited implementation of these methods would suffice. However, any object implementing IHashCodeProvider can be passed to a Hashtable constructor, and that hash function is used for all objects in the table. The objects used as keys in a Hashtable must implement or inherit the Object.GetHashCode and Object.Equals methods. msdn.microsoft.com /library/en-us/cpref/html/frlrfSystemCollectionsHashtableClassTopic.asp?frame=true   (15312 words)

JavaMail API documentation: Class Address Subclasses should provide an implementation of this method that supports value equality (do the two Address objects represent the same destination?), not object reference equality. Subclasses will typically be serializable so that (for example) the use of Address objects in search terms can be serialized along with the search terms. This abstract class models the addresses in a message. java.sun.com /products/javamail/javadocs/javax/mail/Address.html   (123 words)

JavaMail API documentation: Class Address Subclasses should provide an implementation of this method that supports value equality (do the two Address objects represent the same destination?), not object reference equality. Subclasses will typically be serializable so that (for example) the use of Address objects in search terms can be serialized along with the search terms. This abstract class models the addresses in a message. java.sun.com /products/javamail/javadocs/javax/mail/Address.html   (123 words)

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