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Conway and Kochen, The Strong Free Will Theorem, published in Notices of the AMS. Volume 56, Number 2, February 2009. Rehmeyer, Julie (August 15, 2008). "Do Subatomic Particles Have Free Will?". Science News. Introduction to the Free Will Theorem, videos of six lectures given by J. H. Conway, Mar. 2009. Wüthrich, Christian (September 2011).
This conjecture is called "weak" because if Goldbach's strong conjecture (concerning sums of two primes) is proven, then this would also be true. For if every even number greater than 4 is the sum of two odd primes, adding 3 to each even number greater than 4 will produce the odd numbers greater than 7 (and 7 itself is equal to 2+2+3).
The theorem of Du Bois-Reymond asserts that this weak form implies the strong form. If L {\displaystyle L} has continuous first and second derivatives with respect to all of its arguments, and if ∂ 2 L ∂ f ′ 2 ≠ 0 , {\displaystyle {\frac {\partial ^{2}L}{\partial f'^{2}}}\neq 0,} then f {\displaystyle f} has two continuous derivatives ...
Goldbach's comet; red, blue and green points correspond respectively the values 0, 1 and 2 modulo 3 of the number. The Goldbach partition function is the function that associates to each even integer the number of ways it can be decomposed into a sum of two primes.
They are called the strong law of large numbers and the weak law of large numbers. [16] [1] Stated for the case where X 1, X 2, ... is an infinite sequence of independent and identically distributed (i.i.d.) Lebesgue integrable random variables with expected value E(X 1) = E(X 2) = ... = μ, both versions of the law state that the sample average
Many mathematical problems have been stated but not yet solved. These problems come from many areas of mathematics, such as theoretical physics, computer science, algebra, analysis, combinatorics, algebraic, differential, discrete and Euclidean geometries, graph theory, group theory, model theory, number theory, set theory, Ramsey theory, dynamical systems, and partial differential equations.
The following scores (in addition to 1, 2, and 4) cannot be made from multiples of 5 and 7 and so are almost never seen in sevens: 3, 6, 8, 9, 11, 13, 16, 18 and 23. By way of example, none of these scores was recorded in any game in the 2014-15 Sevens World Series .
On the other hand, () is "the number of ways to arrange flags on flagpoles", [8] where all flags must be used and each flagpole can have any number of flags. Equivalently, this is the number of ways to partition a set of size n {\displaystyle n} (the flags) into x {\displaystyle x} distinguishable parts (the poles), with a linear order on the ...