Geocentric model wasn't until Kepler demonstrated a physical observation that could show that the physical sun is directly involved in determining an orbit that a new model was required. The Ptolemaic order of spheres from Earth outward is: Ptolemy did not invent or work out this order, which aligns with the ancient Seven Heavens religious cosmology common to the major Eurasian religious traditions. It also follows the decreasing orbital periods of the moon, sun, planets and stars. Muslim astronomers generally accepted the Ptolemaic system and the geocentric model, but by the 10th century texts appeared regularly whose subject matter was doubts concerning
Central limit theorem possible values. The law of large numbers as well as the central limit theorem are partial solutions to a general problem: "What is the limiting behaviour of as approaches infinity?" In mathematical analysis, asymptotic series are one of the most popular tools employed to approach such questions. Suppose we have an asymptotic expansion of : Dividing both parts by and taking the limit will produce , the coefficient of the highest-order term in the expansion, which represents the rate at which changes in its leading term. Informally, one can say: " grows approximately as ". Taking the difference between and