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This is an accepted version of this page This is the latest accepted revision, reviewed on 17 January 2025. Observation that in many real-life datasets, the leading digit is likely to be small For the unrelated adage, see Benford's law of controversy. The distribution of first digits, according to Benford's law. Each bar represents a digit, and the height of the bar is the percentage of ...
The tendency for an initial segment of data to show some bias that drops out later, one example in number theory being Kummer's conjecture on cubic Gauss sums; The strong law of small numbers, an observation made by the mathematician Richard K. Guy: "There aren't enough small numbers to meet the many demands made of them."
Angular unconformities can occur in ash fall layers of pyroclastic rock deposited by volcanoes during explosive eruptions. In these cases, the hiatus in deposition represented by the unconformity may be geologically very short – hours, days or weeks.
Insensitivity to sample size is a cognitive bias that occurs when people judge the probability of obtaining a sample statistic without respect to the sample size.For example, in one study, subjects assigned the same probability to the likelihood of obtaining a mean height of above six feet [183 cm] in samples of 10, 100, and 1,000 men.
For this reason, it is more accurately called "Pólya's problem". The size of the smallest counterexample is often used to demonstrate the fact that a conjecture can be true for many cases and still fail to hold in general, [ 2 ] providing an illustration of the strong law of small numbers .
Although the radix conversion from decimal floating-point to binary floating-point only incurs a small relative error, catastrophic cancellation may amplify it into a much larger one: double x = 1.000000000000001 ; // rounded to 1 + 5*2^{-52} double y = 1.000000000000002 ; // rounded to 1 + 9*2^{-52} double z = y - x ; // difference is exactly ...
Hutton hit on a variety of ideas to explain the rock formations he saw, and, after a quarter century of work, [1] he read his paper, Theory of the Earth; or an Investigation of the Laws Observable in the Composition, Dissolution and Restoration of Land upon the Globe, to the Royal Society of Edinburgh on 7 March and 4 April 1785.
One example Guy gives is the conjecture that is prime—in fact, a Mersenne prime—when is prime; but this conjecture, while true for = 2, 3, 5 and 7, fails for = 11 (and for many other values). Another relates to the prime number race : primes congruent to 3 modulo 4 appear to be more numerous than those congruent to 1; however this is false ...