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Topic: Equality (mathematics)

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In the News (Tue 22 Jan 19)

  Mathematics as a language
To help you appreciate the expressive power of the modern mathematical language, and as a tribute to those who achieved so much without it, I collected a few samples of (original but translated) formulation of theorems and their equivalents in modern math language.
The area of any circle is equal to a right-angled triangle in which one of the sides about the right angle is equal to the radius, and the other to the circumference, of the circle.
As a matter of fact, mathematical language is by far more accurate than any other one may think of.
www.cut-the-knot.org /language   (865 words)

  Encyclopedia: Equality (mathematics)
In mathematics, one often (not quite always) distinguishes between an identity, which is an assertion that two expressions are equal regardless of the values of any variables that occur within them, and an equation, which may be true for only some (or none) of the values of any such variables.
In mathematics, the concept of binary relation, sometimes called dyadic relation, is exemplified by such ideas as is greater than and is equal to in arithmetic, or is congruent to in geometry, or is an element of or is a subset of in set theory.
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.
www.nationmaster.com /encyclopedia/Equality-(mathematics)   (2174 words)

 MSN Encarta - Mathematics
Mathematics finally became a field in its own right with the development of calculus by English mathematician Isaac Newton and German philosopher and mathematician Gottfried Wilhelm Leibniz during the 17th century and the creation of rigorous mathematical analysis during the 18th century by French mathematician Augustin Louis Cauchy and his contemporaries.
Social scientists also use mathematical techniques, primarily probability and statistics, to help resolve uncertainty about questions such as how various factors affect human behavior, how these variable factors are related, and how groups differ in their responses.
Pure mathematics is the study of abstract relationships, whereas applied mathematics applies mathematical analysis to real-world problems, such as the rate of global warming.
encarta.msn.com /encnet/refpages/RefArticle.aspx?refid=761578291   (1328 words)

 Equality (mathematics)
In mathematics, two mathematical objects are considered equal if they are precisely the same in every way.
A statement that two expressions denote equal quantities is an equation.
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.
www.sciencedaily.com /encyclopedia/equality__mathematics_   (800 words)

 Facts about topic: (Equality (mathematics))   (Site not responding. Last check: 2007-10-16)
In mathematics (A science (or group of related sciences) dealing with the logic of quantity and shape and arrangement), two mathematical objects are considered equal if they are precisely the same in every way.
A statement that two expression (Expression without words) s denote equal quantities is an equation (A mathematical statement that two expressions are equal).
This property is generally used in mathematical proof (Proof of a mathematical theorem) s as an intermediate step.
www.absoluteastronomy.com /encyclopedia/e/eq/equality_(mathematics).htm   (792 words)

 [No title]   (Site not responding. Last check: 2007-10-16)
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.
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.
As it happens, two polygons are equal in Euclid's sense (i.e., they were scissors-congruent) if and only if their areas are equal, but the corresponding conjecture for polyhedra is false.
www.math.rochester.edu /people/faculty/rarm/plato.html   (2608 words)

 Eq Eqbal Ahmad Eqbal Ahmad Eqerem Spahia Equal Equal math Equal mathematics Equal maths   (Site not responding. Last check: 2007-10-16)
Equal temperament - Equal temperament is a scheme of in...
Equality (mathematics) - In, two mathematical objects are considered equal...
Equality of outcome - Equality of outcome is a basic form of...
www.geodatabase.de /?Eq   (860 words)

 Mathematics Multicultural Education Bibliography   (Site not responding. Last check: 2007-10-16)
Most articles are not written by mathematics educators and many articles do not directly refer to mathematics or mathematics education, but the collection does offer relevant studies and theories for the mathematics education community.
According to Bishop, mathematics continues to have the status of a culture-free phenomenon in the otherwise turbulent waters of education and imperialism.
On the basis of the correlation between the Mathematics Anxiety Scale and the Math Anxiety Scale and correlations among the Fennma-Sherman Mathematics Attitude Scales and these measures, the researchers were unable to conclude for this sample of math-anxious individuals that the MARS and MAS measure the same construct.
jwilson.coe.uga.edu /DEPT/Multicultural/MEBib94.html   (13379 words)

 MSN Encarta - Search Results - equality
“equal protection of the laws”, mathematical equality, discrimination, affirmative action, equality rights in Canada, gender equality, in...
Equation, statement of an equality between two expressions, used in almost all branches of pure and applied mathematics and in the physical,...
Identify the property of equality used in the following statement.
ca.encarta.msn.com /equality.html   (160 words)

 On the parallel between mathematics and morals
Insight into the necessities of mathematics is apt for training the mind to love the necessities of ethics, and hence motivates the ruler to make this world conform to those necessities, to the degree that that is possible.
Equality is still a fundamental value of the law, called upon in cases where legally established but unjust practices need to be set aside.
Fundamental to the principles is equality: they are `the principles that free and rational persons concerned to further their own interests would accept in an initial position of equality as defining the fundamental terms of their association’.
web.maths.unsw.edu.au /~jim/matheth.html   (7467 words)

 Supreme Alphabet   (Site not responding. Last check: 2007-10-16)
Supreme mathematics is an alleged system of understanding numbers alongside concepts that are used along with the supreme alphabet as tools to unlocking the keys to reality and/or the universe.
Equality is achieved by teaching others Knowledge and Wisdom, making it Understood thru Understanding.
To manifest from Knowledge to Born, which is the law of mathematics.
www.blackapologetics.com /mathdetail.html   (345 words)

 Writing mathematics
Mathematics is all about implications, statements of the form "assuming that X, we have Y", or "if X then Y", or "since X is true, Y must hold", or "because we know X, Y follows".
Equality means equality, 5 means 5, the Riemann integral is a Riemann integral whether the person reading what you wrote is a Romanian, a freemason, or a vegetarian.
This insistence on accuracy is not some type of malice, or the professor's way of having fun; mathematics simply cannot exist without the rigor of meaning exactly what you say, and your papers cannot be fairly judged in any other manner.
www.math.niu.edu /~behr/Teaching/writing.html   (1061 words)

 Wikinfo | Equality
For the mathematical meaning, see either equation or equality (mathematics).
Equality is a social state of affairs in which certain different people have the same social status in a certain respect.
For example, one may consider equality of the sexes in opportunities for employment; the people in question are men and women (contrasted) and the social situation is the search for a job.
www.wikinfo.org /wiki.php?title=Equality   (156 words)

 All Elementary Mathematics - Study Guide - Algebra - Equations: common information...
Equality - two expressions (numerical or literal ones), jointed by sign ” = “.
Identity - a valid numerical equality or a literal equality, valid at any numerical values of letters, contained in it.
E x a m p l e s : 1) A numerical equality 4 · 7 + 2 = 30 is an identity.
www.bymath.com /studyguide/alg/sec/alg11.html   (217 words)

 Equity vs. Equality   (Site not responding. Last check: 2007-10-16)
He makes numerous strong arguments that "equality" is not synonymous with "equity" and, thus, rather than striving for equality amongst groups of people we should work towards equitable inequalities that reflect the needs and strengths of the various groups.
In the case presented earlier of mathematics as an elitist field, this dichotomy would indicate that the popular view of the subject itself should be changed to reflect the importance of mathematics in everyday life and the contributions of all groups to its development.
By looking to equality and understanding the reasons behind inequalities, we can adjust our schools, our subjects, our very understanding to create equity and move toward a world where equality in the aggregate is a true indicator of justice.
www.mste.uiuc.edu /hill/papers/equity.html   (688 words)

 Equality For All - Author(s): Donna M. Mucks - Grade Level: 7/8 - Subject Area: Math - Students learn the formal steps ...
Extend this discussion to where equality occurs beyond Math class, to solidify the idea of equality and how things do not have to look the same to be equal.
Leading into a discussion of the addition property of equality, and why it is important to recognize and preserve equality in Mathematics.
Mathematically complete and accurate and insightful beyond the topic studied in the unit.
www.connected-learning.org /Products/dmuckslu2.htm   (2293 words)

 Equals sign -   (Site not responding. Last check: 2007-10-16)
The invention of the equals sign is commemorated in St Mary's Church, Tenby, Wales.
A symbol used to denote items that are approximately equal is ≈, and the symbol used to denote when items are not equal is ≠; (most programming languages, which are limited to the ASCII character set, use "!=" or "<>" to represent "not equal to"; "!=" has carried over into newsgroups and internet forums).
In programming languages, the equal sign may either denote a boolean operator to test equality of values (sometimes a double equal sign ==), or it may denote an assignment (sometimes denoted with a colon equals :=).
www.grohol.com /psypsych/Equal_sign   (434 words)

 Foot Soldiers   (Site not responding. Last check: 2007-10-16)
Knowledge manifested through the wisdom, be balanced out on a scale of equality which is saying just-I-see-equality.
JEWEL #6 EQUALITY: is to deal equal with one another and all things.
Equality is to be equaling in all ways like Allah only saying, "no man is better than another."
www.angelfire.com /hiphop/footsoldiers/12jewels.htm   (689 words)

 Philosophy of Real Mathematics
Bernays is perhaps best known for his collaboration with David Hilbert in their studies of the foundations of mathematics.
Not only is Hilbert's axiomatic method praised for its importance to mathematics, but at the end of the piece it is promoted as important to physics too, providing the simplest presentation of relativity theory, and pointing Hilbert to a way to unify this theory with electrodynamics, carried further by Weyl.
Not only is it evidently important for the axiomatic formulation of mathematics, but it is looking very likely that it will play a critical role in whichever reconciliation of general relativity and quantum field theory wins out.
www.dcorfield.pwp.blueyonder.co.uk /blog.html   (2918 words)

 approximate equality - a Whatis.com definition   (Site not responding. Last check: 2007-10-16)
Approximate equality is a concept used primarily in physics and engineering, and also occasionally in mathematics.
In experimental physics and engineering, approximate equality is the rule, because measurements of physical quantities and phenomena are seldom exact.
In many cases, the ordinary equality symbol (=) is used in situations where, to be rigorous, the approximate equality sign ought to be used.
whatis.techtarget.com /definition/0,,sid9_gci822424,00.html   (302 words)

 OEF fractions
Equal fractions Ia Among the fractions presented below, find that are equal.
Equal fractions Ib Among the fractions presented below, find that are equal.
Equal fractions Ic Among the fractions presented below, find that are equal.
wims.unice.fr /wims/es_H2~algebra~oeffraction.en.html   (245 words)

 NCSM - Manipulatives to Concepts to References
Mathematics Teaching in the Middle School, September 2001, 7:1, 20-25.
Mathematics Teaching in the Middle School, December 2000, 6:4, 222-225, 233-235.
Mathematics Teaching in the Middle School, November 2000, 6:3, 164-166, 180-184.
mathforum.org /ncsm/NCSMPublications/2000/MTCR_Mid_A-C.html   (2517 words)

 Weaving Gender Equity - Challenge of the Month   (Site not responding. Last check: 2007-10-16)
For many years, mathematics classrooms operated on the understanding that all students should receive the same thing at the same time in the same way.
In standards-based classrooms, students are encouraged to solve math problems with multiple strategies; assessment tools include portfolios, journals, teacher observation, and exams with multiple kinds of question structure; and students discover their own paths of understanding through group discussion, the use of manipulatives, and real-life problem solving scenarios.
She may then show the whole class the traditional algorithm and expect everyone to master that method as well (an equality model where students are all using the same strategy at the same time).
www.terc.edu /wge/challengejuly.html   (454 words)

 How The Game Is Played
Note that the mathematical concept of equality is not the same mathematical concept as identity.
And if equality is an abstract concept that has no physical reality, neither does anything built ontop of it, which is the entire body of mathematics.
But I also contend that its beauty and purity come from the fact that it is entirely artificial, a logical construct of the human mind, with no basis in the physical world at all.
blogs.sun.com /roller/page/gameguy?entry=the_incredible_abstractness_of_mathematics   (1328 words)

Immediately the article drew the ire of the Commission for Racial Equality which sent the article to the police claiming it to be a case of incitement to racial hatred.
His employer, that monument to freedom of speech, the BBC, showing itself to be both mean and censorious, collapsed under the pressure to stop its presenters from saying anything offensive about a religion, or its adherents, and suspended him.
The racial composition of the UK Commission for Racial Equality may be of interest to readers.
www.quebecoislibre.org /04/040207-6.htm   (2351 words)

 Nat' Academies Press, Adding It Up: Helping Children Learn Mathematics (2001)
These findings, which surprised most teachers, have led them to begin to listen to their students, and a number of teachers have engaged their students in a discussion of the reasons for their responses.
The teachers’ experiences have precipitated a discussion in the workshop of how students are thinking about equality and how these misconceptions might have been acquired.
Properties of equality that the teachers have not usually examined carefully before emerge in their discussions of students’ conceptions and misconceptions in using the equals sign.
www.nap.edu /books/0309069955/html/390.html   (653 words)

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