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The degree of the graph of a rational function is not the degree as defined above: it is the maximum of the degree of the numerator and one plus the degree of the denominator. In some contexts, such as in asymptotic analysis, the degree of a rational function is the difference between the degrees of the numerator and the denominator.
Thus, a planar graph has genus 0, because it can be drawn on a sphere without self-crossing. The non-orientable genus of a graph is the minimal integer n such that the graph can be drawn without crossing itself on a sphere with n cross-caps (i.e. a non-orientable surface of (non-orientable) genus n). (This number is also called the demigenus.)
A polynomial function is one that has the form = + + + + + where n is a non-negative integer that defines the degree of the polynomial. A polynomial with a degree of 0 is simply a constant function; with a degree of 1 is a line; with a degree of 2 is a quadratic; with a degree of 3 is a cubic, and so on.
Given a function: from a set X (the domain) to a set Y (the codomain), the graph of the function is the set [4] = {(, ()):}, which is a subset of the Cartesian product.In the definition of a function in terms of set theory, it is common to identify a function with its graph, although, formally, a function is formed by the triple consisting of its domain, its codomain and its graph.
The graph of a differentiable function is homeomorphic to the domain of the function. A differentiable parametrization of a curve is a homeomorphism between the domain of the parametrization and the curve. A chart of a manifold is a homeomorphism between an open subset of the manifold and an open subset of a Euclidean space.
Gardner, Martin (1994), "Hole in the Sphere", My best mathematical and logic puzzles, Dover Publications, p. 8 Jones, Samuel I. (1912), Mathematical Wrinkles for Teachers and Private Learners , Norwood, MA: J. B. Cushing Co. Problem 132 asks for the volume of a sphere with a cylindrical hole drilled through it, but does not note the invariance ...
(Reuters) -U.S. President-elect Donald Trump said on Monday there would be "hell to pay" in the Middle East if hostages held in the Gaza Strip were not released prior to his Jan. 20 inauguration.
For a torus, the first Betti number is b 1 = 2 , which can be intuitively thought of as the number of circular "holes" Informally, the kth Betti number refers to the number of k-dimensional holes on a topological surface. A "k-dimensional hole" is a k-dimensional cycle that is not a boundary of a (k+1)-dimensional object.