Search results
Results From The WOW.Com Content Network
The free will theorem of John H. Conway and Simon B. Kochen states that if we have a free will in the sense that our choices are not a function of the past, then, subject to certain assumptions, so must some elementary particles. Conway and Kochen's paper was published in Foundations of Physics in 2006. [1]
Stone's theorem on one-parameter unitary groups (functional analysis) Stone–Tukey theorem ; Stone–von Neumann theorem (functional analysis, representation theory of the Heisenberg group, quantum mechanics) Stone–Weierstrass theorem (functional analysis) Strassmann's theorem (field theory) Strong perfect graph theorem (graph theory)
This is a list of axioms as that term is understood in mathematics. In epistemology , the word axiom is understood differently; see axiom and self-evidence . Individual axioms are almost always part of a larger axiomatic system .
If there are n-1 phantoms at 0, then the median rule returns the minimum of all real votes. If there are n-1 phantoms at 100, then the median rule returns the maximum of all real votes. If there are n-1 phantoms at 50, then the median rule returns 50 if some ideal points are above and some are below 50; otherwise, it returns the vote closest to 50.
Littlewood's three principles are quoted in several real analysis texts, for example Royden, [2] Bressoud, [3] and Stein & Shakarchi. [4] Royden [5] gives the bounded convergence theorem as an application of the third principle. The theorem states that if a uniformly bounded sequence of functions converges pointwise, then their integrals on a ...
Thus, in frequentist decision theory it is sufficient to consider only (generalized) Bayes rules. Conversely, while Bayes rules with respect to proper priors are virtually always admissible, generalized Bayes rules corresponding to improper priors need not yield admissible procedures. Stein's example is one such famous situation.
Arrow's theorem is not related to strategic voting, which does not appear in his framework, [3] [1] though the theorem does have important implications for strategic voting (being used as a lemma to prove Gibbard's theorem [15]). The Arrovian framework of social welfare assumes all voter preferences are known and the only issue is in ...
An abelian group with Ext 1 (A, Z) = 0 is called a Whitehead group; MA + ¬CH proves the existence of a non-free Whitehead group, while V = L proves that all Whitehead groups are free. In one of the earliest applications of proper forcing, Shelah constructed a model of ZFC + CH in which there is a non-free Whitehead group. [12] [13]