commutative

commutative : In mathematics, commutativity is the property that changing the order of something does not change the end result. It is a fundamental property of many binary operations, and many mathematical proofs depend on it. The commutativity of simple operations, such as multiplication and addition of numbers, was for many years implicitly assumed and the property was not named until the 19th century when mathematicians began to formalize the theory of mathematics. The commutative property (or commutative law) is a property associated with binary operations and functions. Similarly, if the commutative property holds for a pair of elements under a certain binary operation then it is said that the two elements commute under that operation. In group and set theory, many algebraic structures are called commutative when certain operands satisfy the commutative property. In higher branches of math, such as analysis and linear algebra the commutativity of well known operations..   More from Wikipedia

commutative : The Journal of Commutative Algebra is an international mathematical journal publishing research papers and expository articles in commutative algebra and closely related fields including algebraic number theory, algebraic geometry, representation theory, semigroups and monoids. The journal..   More from Wikipedia

commutative : Algebraic geometry is a branch of mathematics which, combines abstract algebra, especially commutative algebra, with geometry. See also: Computers & Math Mathematics Math Puzzles It can be seen as the study of solution sets of systems of polynomials. When there is more than one variable, geometric considerations enter and are important to understand the phenomenon. One can say that the subject starts where equation solving leaves off, and it becomes at least as important to understand the totality of solutions of a system of equations as to find some solution; this does lead into some of the deepest waters in the whole of mathematics, both conceptually and in terms of technique.. For more information about the topic Algebraic geometry, read the full article at Wikipedia.org, or see the following related articles: Geometry — Geometry arose as the field of knowledge dealing with spatial relationships. Geometry was one of the two fields of pre-modern mathematics, the other ...  > read....   More from Science Daily

commutative : Topology is a branch of mathematics, an extension of geometry. See also: Space & Time Astronomy ESA Computers & Math Computer Modeling Mathematics Mathematical Modeling Topology begins with a consideration of the nature of space, investigating both its fine structure and its global structure. Topology builds on set theory, considering both sets of points and families of sets. The word topology is used both for the area of study, and for a family of sets with certain properties described below. Of particular importance in the study of topology are functions or maps that are continuous. These functions stretch space without tearing it apart or sticking distinct parts together.. For more information about the topic Topology, read the full article at Wikipedia.org, or see the following related articles: Probability theory — Probability theory is the mathematical study of phenomena characterized by randomness or uncertainty. More precisely, probability is used for ...  > read more Geome....   More from Science Daily

  Access full lesson containing this video at: www.yourteacher.com Students learn the following addition properties: the commutative property of addition, which states that a + b = b + a, the associative property of addition, which states that (a + b) + c = a + (b + c), and the identity property of addition, which states that a + 0 = a.

  Learn math for fun. That sounds pretty lame. This video is about the different things that some math words mean. That sounds lame too. Just watch it.

Question : I have a project I'm working on and I can't seem to find how motors relate to Heat Recovery Ventilators anywhere. And are electronically commutative motors just your basic electromagnetic motor? Any help would be really appreciated-- (sources for info would be really awesome too) thanks!

Answer : I thought I should let you read the Patent of an electronically commutative motor....!! LOL http://www.freepatentsonline.com/5457366.html Now lets try this in English: Imagine a "standard" forced air heating system. The fan motor is either "On" of "Off", right? But this is often not necessary, and the noise can be annoying. An electronically commutative motor (ECM) is - as you suspect - very much a "basic electromagnetic motor", but it is controlled by an electronic circuitry which takes readings from sensors and "decides" how fast the fan motor *really needs* to turn, and then controls the motor speed accordingly. This saves electricity, increases the (power-) efficiency of the whole system, and cuts down on humming noise as well.... But as so often with these "good things", you have to spend money upfront (for the control electronics), in order to save a few dollars over the coming years.......   More from Yahoo Answers

Question : The commutative and associative properties. Which one of these properties do you think is the most practical or useful? You may refer to math or everyday life. If you could explain the reasons for your opinion that would be great. Support your reasons with examples if possible.

Answer : An interesting question. My answer depends quite a lot on the context. If you mean in a mathematical research type of sense, then I would say associativity is more useful. We know of a good number of examples of systems which are non-commutative. For a few examples, consider matrices, quaternions, functions under composition, etc. In fact, the commutative (or "abelian") groups are somewhat boring to study in abstract algebra. On the other hand, associativity is in every example I mentioned above. Almost all of the common sets and operations have associativity. Well, I suppose subtraction and division are nonassociative, but these are inverses of addition and multiplication, so they don't really count (so far as I'm concerned). One good example of a nonassociative operation is the cross product of vectors. But that's about all that I can think of. Notice that the cross product is also noncommutative. If I think of this in a more everyday setting though, I think it's ha....   More from Yahoo Answers