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Division algorithm (4643 bytes)
24: We claim that ''S'' contains at least one nonnegative integer. There are two cases to consider. 26: ..., and by the [[Archimedean property]], there is a nonnegative integer ''n'' such that (−''b'')''n'' ≥ ... 27: ...hen again by the Archimedean property, there is a nonnegative integer ''n'' such that ''dn'' ≥ −''a'',... 29: ...ple]], and deduce that ''S'' contains a ''least'' nonnegative integer ''r''. If we now let ''q'' = (''a'' &minu... 31: ...ality holds because of the choice of ''r'' as a ''nonnegative'' integer. To show the last (strict) inequality, ... Trinomial expansion (737 bytes) 5: ...ger and the sum is taken over all combinations of nonnegative indices ''i'', ''j'', and ''k'' such that ''i''+'... Generalized permutation matrix (616 bytes) 8: ...are both nonnegative matrices (i.e. matrices with nonnegative entries), then the matrix is a generalized permut... Mixture density (1647 bytes) 3: ...y density function with respect to ''x''. Given a nonnegative function ''w'' such that ''w''(''a'') integrates ... 16: ...ng other than 1. It can be shown that if ''w'' is nonnegative and integrates to 1, then the function ''q'' as d... Penrose-Hawking singularity theorems (345 bytes) 1: ...nd the [[Stress-energy tensor|energy density]] is nonnegative, then there exist [[geodesic]]s of finite length ... Muirhead's inequality (2559 bytes) 11: define the "''a''-mean" [''a''] of nonnegative real numbers ''x''<sub>1</sub>, ..., ''x''<sub>''... 21: ... a doubly stochastic matrix is a square matric of nonnegative real entries in which the sum of the entries in e... Negative and non-negative numbers (6706 bytes) 11: ... [[integer]]s from [[zero]] on upwards, and the ''nonnegative reals'' are all the [[real number]]s from [[zero]... 13: ...lled '''nonnegative''' if every entry of ''A'' is nonnegative. 15: ...terminant]] of every square submatrix of ''A'' is nonnegative. Polynomial sequence (657 bytes) 1: ... a [[sequence]] of [[polynomial]]s indexed by the nonnegative integers 0, 1, 2, 3, ..., in which each index is ... Instanton (2116 bytes) 17: ...integral of a nonnegative [[integrand]] is always nonnegative, Integral test for convergence (584 bytes) 2: ... test infinite [[series (mathematics)|series]] of nonnegative terms for [[convergence]]. Bijection (5526 bytes) 33: ...main and codomain both restricted to only the ''[[nonnegative]]'' real numbers, then the function <var>h</var> ... 34: ...bsp;= <var>x</var><sup>2</sup> to get exactly one nonnegative real solution <var>x</var> = √<var>y</... Surjection (4796 bytes) 25: ... but with the codomain restricted to only the ''[[nonnegative]]'' real numbers, then the function <var>h</var> ... 26: This is because, given an arbitrary nonnegative real number <var>y</var>, we can solve <var>y</va... Normalizing constant (3135 bytes) 5: ... constant''' is a constant by which an everywhere nonnegative function must be multiplied in order to get a [[p... 23: is a probability mass function on the set of all nonnegative integers. This is the probability mass function ... Highest weight representation and lowest weight representation (619 bytes) 1: ...total ordering]] of this vector space such that a nonnegative [[linear combination]] of positive vectors with a... Compositional data (997 bytes) 1: ...in which each [[data point]] is an ''n''-tuple of nonnegative numbers whose sum is 1. Typically each of the ''... Representation theory of SU(2) (3744 bytes) 47: ... to be -λ. This means λ has to be a nonnegative integer multiple of half. Every weight is a numbe... 49: This construction also shows for any given nonnegative integer multiple of half λ, all finite dim... Injective function (6067 bytes) 30: ...'is'' injective. This is because, given arbitrary nonnegative real numbers <var>x</var> and <var>x'</var>, if <... Hahn-Jordan decomposition (1008 bytes) 3: ...</sup> and Ω<sup>-</sup>, such that μ is nonnegative for every set contained in Ω<sup>+</sup> an... Dirichlet principle (1073 bytes) 15: Since the Dirichlet integral is nonnegative, the existence of an [[infimum]] is guaranteed. T... Markov network (1008 bytes) 1: ... set of all assignments to the variables to the [[nonnegative]] [[real numbers]]. It is similar to a [[Bayesian...
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