Search results
Results from the WOW.Com Content Network
The word problem for an algebra is then to determine, given two expressions (words) involving the generators and operations, whether they represent the same element of the algebra modulo the identities. The word problems for groups and semigroups can be phrased as word problems for algebras. [1]
For instance, if the one solving the math word problem has a limited understanding of the language (English, Spanish, etc.) they are more likely to not understand what the problem is even asking. In Example 1 (above), if one does not comprehend the definition of the word "spent," they will misunderstand the entire purpose of the word problem.
A similar effect is available for peak-like functions, such as Gaussian, Exponentially modified Gaussian and other functions with derivatives at integration limits that can be neglected. [10] The evaluation of the full integral of a Gaussian function by trapezoidal rule with 1% accuracy can be made using just 4 points. [11]
Some sources use the term proper trapezoid to describe trapezoids under the exclusive definition, analogous to uses of the word proper in some other mathematical objects. [6] Others [3] define a trapezoid as a quadrilateral with at least one pair of parallel sides (the inclusive definition [7]), making the parallelogram a special type of trapezoid.
In group theory, a word is any written product of group elements and their inverses. For example, if x, y and z are elements of a group G, then xy, z −1 xzz and y −1 zxx −1 yz −1 are words in the set {x, y, z}. Two different words may evaluate to the same value in G, [1] or even in every group. [2]
Any non-self-crossing quadrilateral with exactly one axis of symmetry must be either an isosceles trapezoid or a kite. [5] However, if crossings are allowed, the set of symmetric quadrilaterals must be expanded to include also the crossed isosceles trapezoids, crossed quadrilaterals in which the crossed sides are of equal length and the other sides are parallel, and the antiparallelograms ...
Comparisons of "trapezium" in both British and American English. Trapezium, plural trapezia, may refer to: . Trapezium, in British and other forms of English, a trapezoid, a quadrilateral that has exactly one pair of parallel sides
In elementary algebra, parentheses ( ) are used to specify the order of operations. [1] Terms inside the bracket are evaluated first; hence 2×(3 + 4) is 14, 20 ÷ (5(1 + 1)) is 2 and (2×3) + 4 is 10. This notation is extended to cover more general algebra involving variables: for example (x + y) × (x − y). Square brackets are also often ...