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In mathematics, the pigeonhole principle states that if n items are put into m containers, with n > m, then at least one container must contain more than one item. [1] For example, of three gloves, at least two must be right-handed or at least two must be left-handed, because there are three objects but only two categories of handedness to put ...
The notation a ≥ b or a ⩾ b or a ≧ b means that a is greater than or equal to b (or, equivalently, at least b, or not less than b). In the 17th and 18th centuries, personal notations or typewriting signs were used to signal inequalities. [2] For example, In 1670, John Wallis used a single horizontal bar above rather than
The red subset = {1,2,3,4} has two maximal elements, viz. 3 and 4, and one minimal element, viz. 1, which is also its least element. In mathematics , especially in order theory , a maximal element of a subset S {\displaystyle S} of some preordered set is an element of S {\displaystyle S} that is not smaller than any other element in S ...
Scitovsky paradox: Using the Kaldor–Hicks criterion, an allocation A may be more efficient than allocation B, while at the same time B is more efficient than A. Service recovery paradox: Successfully fixing a problem with a defective product may lead to higher consumer satisfaction than in the case where no problem occurred at all.
2001: four different authors published different implementations of a distributed hash table. The Super Kamiokande and SNOLAB collaborations, whose findings were published in 1998 and 2001 respectively, both proved that neutrinos have mass. As a result, the 2015 Nobel Prize in Physics was shared by Takaaki Kajita of Japan and Arthur B. McDonald ...
As more symptoms are considered, it becomes increasingly likely that the drug will appear to be an improvement over existing drugs in terms of at least one symptom. In both examples, as the number of comparisons increases, it becomes more likely that the groups being compared will appear to differ in terms of at least one attribute.
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Singmaster's conjecture is a conjecture in combinatorial number theory, named after the British mathematician David Singmaster who proposed it in 1971. It says that there is a finite upper bound on the multiplicities of entries in Pascal's triangle (other than the number 1, which appears infinitely many times).