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A coordinate singularity occurs when an apparent singularity or discontinuity occurs in one coordinate frame, which can be removed by choosing a different frame. An example of this is the apparent singularity at the 90 degree latitude in spherical coordinates. An object moving due north (for example, along the line 0 degrees longitude) on the ...
In mathematics, singularity theory studies spaces that are almost manifolds, but not quite. A string can serve as an example of a one-dimensional manifold, if one neglects its thickness. A singularity can be made by balling it up, dropping it on the floor, and flattening it.
The Singularity Is Near, a 2005 book by Ray Kurzweil on the technological singularity; The Singularity Is Nearer, a 2024 sequel to Ray Kurzweil's 2005 book; Singularity (comics), the Marvel Comics character; Singularity, a 2023 novel by Jeremy Robinson, which is the finale of the "Infinite Timeline"
Singularity functions have been heavily studied in the field of mathematics under the alternative names of generalized functions and distribution theory. [ 1 ] [ 2 ] [ 3 ] The functions are notated with brackets, as x − a n {\displaystyle \langle x-a\rangle ^{n}} where n is an integer.
For more complicated singularities, such as x 2 = y m z n which is singular along x = yz =0, blowing up the worst singularity at the origin produces the singularities x 2 = y m+n−2 z n and x 2 = y m z m+n−2 which are worse than the original singularity if m and n are both at least 3.
Specifically, the singularity is such that |K(x, y)| is of size |x − y| −n asymptotically as |x − y| → 0. Since such integrals may not in general be absolutely integrable, a rigorous definition must define them as the limit of the integral over |y − x| > ε as ε → 0, but in practice this is a technicality.
In mathematics, and particularly singularity theory, the Milnor number, named after John Milnor, is an invariant of a function germ. If f is a complex-valued holomorphic function germ then the Milnor number of f, denoted μ(f), is either a nonnegative integer, or is infinite. It can be considered both a geometric invariant and an algebraic ...
The singularity at the center of a Schwarzschild black hole is an example of a strong singularity. Space-like singularities are a feature of non-rotating uncharged black holes as described by the Schwarzschild metric , while time-like singularities are those that occur in charged or rotating black hole exact solutions.