Mathematical concept based on the idea of closeness, used mainly in studying the behaviour of functions close to values at which they are undefined. For example, the function 1/math.x is not defined at math.x = 0. For positive values of math.x, as math.x is chosen closer and closer to 0, the value of 1/math.x begins to grow rapidly, approaching infinity as a limit. This interplay of action and reaction as the independent variable moves closer to a given value is the essence of the idea of a limit. Limits provide the means of defining the derivative and integral of a function.
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In statistics, any of several fundamental theorems in probability. Originally known as the law of errors, in its classic form it states that the sum of a set of independent random variables will approach a normal distribution regardless of the distribution of the individual variables themselves, given certain general conditions. Further, the mean (see mean, median, and mode) of the normal distribution will coincide with the (arithmetic) mean of the (statistical) means of each random variable.
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Minimum distance at which a large natural satellite can orbit its primary body without being torn apart by tidal forces. If satellite and primary are of similar composition, the theoretical limit is about 2.5 times the radius of the larger body. The rings of Saturn, for example, lie inside Saturn's Roche limit and may be the debris of a demolished moon. The limit was first calculated by the French astronomer Édouard Roche (1820–53) in 1850.
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