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The fixed point iteration x n+1 = cos x n with initial value x 1 = −1.. An attracting fixed point of a function f is a fixed point x fix of f with a neighborhood U of "close enough" points around x fix such that for any value of x in U, the fixed-point iteration sequence , (), (()), ((())), … is contained in U and converges to x fix.
The Banach fixed-point theorem (1922) gives a general criterion guaranteeing that, if it is satisfied, the procedure of iterating a function yields a fixed point. [2]By contrast, the Brouwer fixed-point theorem (1911) is a non-constructive result: it says that any continuous function from the closed unit ball in n-dimensional Euclidean space to itself must have a fixed point, [3] but it doesn ...
For any noncompact topological space X the (Alexandroff) one-point compactification αX of X is obtained by adding one extra point ∞ (often called a point at infinity) and defining the open sets of the new space to be the open sets of X together with the sets of the form G ∪ {∞}, where G is an open subset of X such that is closed and compact.
Linear or point-projection perspective (from Latin perspicere 'to see through') is one of two types of graphical projection perspective in the graphic arts; the other is parallel projection. [ citation needed ] [ dubious – discuss ] Linear perspective is an approximate representation, generally on a flat surface, of an image as it is seen by ...
The vanishing point may also be referred to as the "direction point", as lines having the same directional vector, say D, will have the same vanishing point. Mathematically, let q ≡ ( x , y , f ) be a point lying on the image plane, where f is the focal length (of the camera associated with the image), and let v q ≡ ( x / h , y ...
In mathematics, a pointed space or based space is a topological space with a distinguished point, the basepoint.The distinguished point is just simply one particular point, picked out from the space, and given a name, such as , that remains unchanged during subsequent discussion, and is kept track of during all operations.
Image credits: Fun-Yellow-6576 #7. My ex roommate and a guy I knew for a decade. We decided that we would switch off cooking/dishes so whoever cooks the other person washes up.
This page was last edited on 16 February 2023, at 11:05 (UTC).; Text is available under the Creative Commons Attribution-ShareAlike 4.0 License; additional terms may apply.
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