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A slab can also be defined as a set of points: [3] {}, where is the normal vector of the planes = and =. Or, if the slab is centered around the origin: [ 4 ] { x ∈ R n ∣ | n ⋅ x | ≤ θ / 2 } , {\displaystyle \{x\in \mathbb {R} ^{n}\mid |n\cdot x|\leq \theta /2\},} where θ = | α − β | {\displaystyle \theta =|\alpha -\beta |} is the ...
A closed half-space is the union of an open half-space and the hyperplane that defines it. The open (closed) upper half-space is the half-space of all (x1, x2, ..., xn) such that xn > 0 (≥ 0). The open (closed) lower half-space is defined similarly, by requiring that xn be negative (non-positive). A half-space may be specified by a linear ...
In mathematics, change of base can mean any of several things: Changing numeral bases, such as converting from base 2 (binary) to base 10 (decimal). This is known as base conversion. The logarithmic change-of-base formula, one of the logarithmic identities used frequently in algebra and calculus. The method for changing between polynomial and ...
Constant term. In mathematics, a constant term (sometimes referred to as a free term) is a term in an algebraic expression that does not contain any variables and therefore is constant. For example, in the quadratic polynomial, The number 3 is a constant term. [1]
In mathematics, a codomain or set of destination of a function is a set into which all of the output of the function is constrained to fall. It is the set Y in the notation f: X → Y. The term range is sometimes ambiguously used to refer to either the codomain or the image of a function. A codomain is part of a function f if f is defined as a ...
The usual order relation on the real numbers is antisymmetric: if for two real numbers and both inequalities and hold, then and must be equal. Similarly, the subset order on the subsets of any given set is antisymmetric: given two sets and if every element in also is in and every element in is also in then and must contain all the same elements ...
The concept of antipodal points is generalized to spheres of any dimension: two points on the sphere are antipodal if they are opposite through the centre. Each line through the centre intersects the sphere in two points, one for each ray emanating from the centre, and these two points are antipodal. The Borsuk–Ulam theorem is a result from ...
Engineering mathematics. Mathematical engineering (or engineering mathematics) is a branch of applied mathematics, concerning mathematical methods and techniques that are typically used in engineering and industry. Along with fields like engineering physics and engineering geology, both of which may belong in the wider category engineering ...