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In mathematics and computer science, the sorting numbers are a sequence of numbers introduced in 1950 by Hugo Steinhaus for the analysis of comparison sort algorithms. These numbers give the worst-case number of comparisons used by both binary insertion sort and merge sort. However, there are other algorithms that use fewer comparisons.
The second number class is the set of ordinals whose predecessors form a countably infinite set. The set of all α having countably many predecessors—that is, the set of countable ordinals—is the union of these two number classes. Cantor proved that the cardinality of the second number class is the first uncountable cardinality. [12]
Every well-ordered set is order-equivalent to exactly one ordinal number, by definition. The ordinal numbers are taken to be the canonical representatives of their classes, and so the order type of a well-ordered set is usually identified with the corresponding ordinal. Order types thus often take the form of arithmetic expressions of ordinals.
The twelve-point system differs from the above only in using the grade A+, to which the value 12.0 is applied. The 1-2-3-4 system Some school districts use a 1-2-3-4 rating system for grades at the elementary (K–5) level, notably many California school districts including The Los Angeles Unified School District (LAUSD) which switched with the ...
Rational number is any number that can be expressed as the quotient or fraction p/q of two integers, with the denominator q not equal to zero. [9] Since q may be equal to 1, every integer is a rational number. The set of all rational numbers is usually denoted by a boldface Q (or blackboard bold).
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[8] [11] These numbers were called Fubini numbers by Louis Comtet, because they count the different ways to rearrange the ordering of sums or integrals in Fubini's theorem, which in turn is named after Guido Fubini. [12] The Bell numbers, named after Eric Temple Bell, count the partitions of a set, and the weak orderings that are counted by the ...
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