A normal is an object such as a line or vector that is perpendicular to a given object. For example, in two dimensions, the normal line to a curve at a given point is the
line perpendicular to the tangent line to the curve at the point.
Multiply (a series, function or item of data) by a factor that makes the norm or some associated quantity such as an integral equal to a desired value (usually 1).
Whole numbers are positive numbers, including zero, without any decimal or fractional parts. They are numbers that represent whole things without pieces. The set of whole numbers is represented mathematically by the set: {0, 1, 2, 3, 4..}.
Odd numbers cannot be divided evenly into groups of two. The number five can be divided into two groups of two and one group of one. Even numbers always end with a digit of 0, 2, 4, 6 or 8. 2, 4, 6, 8, 10,
12, 14, 16, 18, 20, 22, 24, 26, 28, 30 are
even numbers. Odd numbers always end with a digit of 1, 3, 5, 7, or 9.
The real function f is an odd function if f(–x)
= – f(x) for all x (in the domain of f). Thus the graph y = f(x) of an odd function is symmetrical about the origin / that is, it has a half-turn symmetry about the origin, because whenever (x,y) lies on the graph then so does (–x, –y).
An injective function or injection or one-to-one function is a function that preserves distinctness: it never maps
distinct elements of its domain to the same element of its codomain. In other words, every element of the function's codomain is the image of at most one element of its domain.
A function for which every element of the range of the function corresponds to exactly one element of the domain. One-to-one is often written 1-1. Note: y = f(x) is a function if it passes the vertical line test. It is a 1-1 function if it passes both the vertical line test
and the horizontal line test.
An open interval does not include its endpoints and is indicated with parentheses. For example, (0,1) means greater than 0 and less than 1. A closed interval is an interval which includes all its limit points and
is denoted with square brackets.
The simplest example is in metric spaces, where open sets can be defined as those sets which contain a ball around each of their points (or, equivalently, a set is open if it doesn't contain any of its boundary
points) / however, an open set, in general, can be very abstract: any collection of sets can be called open.
Order theory is a branch of mathematics, which investigates the intuitive notion of order using binary relations. It provides a formal framework for describing statements such as "this is less than that" or "this precedes that".
In mathematics, an ordered pair (a, b) is a pair of objects. The order in which the objects appear in the pair is significant: the ordered pair (a, b) is different from the ordered pair (b, a) unless a = b.
Angular position, or attitude of an object such as a line, plane or rigid body is part of the description of how it is placed in the space it occupies. Namely, it is the imaginary rotation that is needed to move
the object from a reference placement to its current placement.
The coordinates for every other point are
based on how far that point is from the origin. At the origin, both x and y are equal to zero, and the x-axis and the y-axis intersect.
Orthogonality is the generalization of the notion of perpendicular to the linear algebra of bilinear forms. Two elements u and v of a vector space with bilinear form B are orthogonal when B = 0. Depending on the
bilinear form, the vector space may contain nonzero self-orthogonal vectors.
Particularly in differential geometry, an osculating plane is a plane in a Euclidean space or affine space which meets a
sub-manifold at a point in such a way as to have a second order of contact at the point.