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In their later 2009 paper, "The Strong Free Will Theorem", [2] Conway and Kochen replace the Fin axiom by a weaker one called Min, thereby strengthening the theorem. The Min axiom asserts only that two experimenters separated in a space-like way can make choices of measurements independently of each other.
1905 Emanuel Lasker's original proof of the Lasker–Noether theorem took 98 pages, but has since been simplified: modern proofs are less than a page long. 1963 Odd order theorem by Feit and Thompson was 255 pages long, which at the time was over 10 times as long as what had previously been considered a long paper in group theory.
The law of truly large numbers (a statistical adage), attributed to Persi Diaconis and Frederick Mosteller, states that with a large enough number of independent samples, any highly implausible (i.e. unlikely in any single sample, but with constant probability strictly greater than 0 in any sample) result is likely to be observed. [1]
[35]: 247-248 The free will theorem of John H. Conway and Simon B. Kochen further establishes that if we have free will, then quantum particles also possess free will. [ 36 ] [ 37 ] This means that starting from the assumption that humans have free will, it is possible to pinpoint the origin of their free will in the quantum particles that ...
The strong exponential time hypothesis implies that it is not possible to find -vertex dominating sets more quickly than in time (). [ 8 ] The exponential time hypothesis implies also that the weighted feedback arc set problem on tournaments does not have a parametrized algorithm with running time O ( 2 o ( OPT ) n O ( 1 ) ) {\textstyle O(2^{o ...
Renewal theory is the branch of probability theory that generalizes the Poisson process for arbitrary holding times. Instead of exponentially distributed holding times, a renewal process may have any independent and identically distributed (IID) holding times that have finite mean. A renewal-reward process additionally has a random sequence of ...
For example, if you had two types of coins valued at 6 cents and 14 cents, the GCD would equal 2, and there would be no way to combine any number of such coins to produce a sum which was an odd number; additionally, even numbers 2, 4, 8, 10, 16 and 22 (less than m=24) could not be formed, either.
The asymptotic equipartition property holds if the process is white, in which case the time samples are i.i.d., or there exists T > 1/2W, where W is the nominal bandwidth, such that the T-spaced time samples take values in a finite set, in which case we have the discrete-time finite-valued stationary ergodic process.