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Namely, the orthogonality relation for polynomials with a weight function, supported on a countable set of points, may be of the form (for instance, for the big q-Jacobi polynomials)
If J additionally is completely continuous then J has a countable set of eigenvalues which can be characterized as minmax and maxmin values of the Rayleigh quotient by the principles of Poincare and of Courant, Fischer and Weyl.
Let X be any countable set and [tau] = cofinite topology then X is [T.
First, if sampling a function f on the countable set X leads to unique and stable reconstruction of f, then when does sampling on the set X' = {[x.
Marino said he first came up with the concept for the game while in a discrete mathematics class, studying such concepts as countable sets and finite mathematics, at Worcester State College.
The lectures went on telling about mathematical formalism and abstract set theory starting with Eider's diagrams or circles from 1761 (Sandifer 2007) and George Boole's logical system (Boolean algebra) from 1854 (Gowers 2008, Wolff 1963), then Georg Cantor's theory of sets and a little about countable sets and transfinite cardinals (Gowers 2008), and after this ending up with Bertrand Russell's famous paradox from 1904 (Gowers 2008, Olesen (13) 2007).