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In computational geometry, an ε-net (pronounced epsilon-net) is the approximation of a general set by a collection of simpler subsets. In probability theory it is the approximation of one probability distribution by another.
An -net or epsilon net in mathematics may refer to: ε-net (computational geometry) in computational geometry and in geometric probability theory ε-net (metric spaces) in metric spaces
As the most restrictive of the definitions above, ε-nets are at least as difficult to construct as ε-packings, ε-coverings, and Delone sets.However, whenever the points of M have a well-ordering, transfinite induction shows that it is possible to construct an ε-net N, by including in N every point for which the infimum of distances to the set of earlier points in the ordering is at least ε.
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This alternative definition is significantly more widespread: machine epsilon is the difference between 1 and the next larger floating point number.This definition is used in language constants in Ada, C, C++, Fortran, MATLAB, Mathematica, Octave, Pascal, Python and Rust etc., and defined in textbooks like «Numerical Recipes» by Press et al.
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