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Examples include the class of all groups, the class of all vector spaces, and many others. In category theory, a category whose collection of objects forms a proper class (or whose collection of morphisms forms a proper class) is called a large category. The surreal numbers are a proper class of objects that have the properties of a field.
Several states have relaxed those requirements since 2008. Florida's class size cap was established over the course of several years, in response to a statewide referendum in 2002 that amended its state constitution. Statewide, class size averages are 15.46 students per class in grades preK-3, 17.75 in grades 4–8, and 19.01 in high school.
930 History of ancient world (to c. 499) 930 History of ancient world to c. 499; 931 China to 420; 932 Egypt to 640; 933 Palestine to 70; 934 South Asia to 647; 935 Mesopotamia and Iranian Plateau to 637; 936 Europe north and west of Italian Peninsula to c. 499; 937 Italy and adjacent territories to 476; 938 Greece to 323; 939 Other parts of ...
The ratio is often used as a proxy for class size, although various factors can lead to class size varying independently of student–teacher ratio (and vice versa). [2] In most cases, the student–teacher ratio will be significantly lower than the average class size. [3] Student–teacher ratios vary widely among developed countries. [4]
In mathematics, the ideal class group (or class group) of an algebraic number field K is the quotient group J K /P K where J K is the group of fractional ideals of the ring of integers of K, and P K is its subgroup of principal ideals. The class group is a measure of the extent to which unique factorization fails in the ring of integers of K.
In computational complexity theory, the class NC (for "Nick's Class") is the set of decision problems decidable in polylogarithmic time on a parallel computer with a polynomial number of processors. In other words, a problem with input size n is in NC if there exist constants c and k such that it can be solved in time O ((log n ) c ) using O ...
In mathematics, a structure on a set (or on some sets) refers to providing it (or them) with certain additional features (e.g. an operation, relation, metric, or topology). Τhe additional features are attached or related to the set (or to the sets), so as to provide it (or them) with some additional meaning or significance.
Class groups of algebraic number fields were among the earliest examples of factor groups, of much interest in number theory. If a group G is a permutation group on a set X , the factor group G / H is no longer acting on X ; but the idea of an abstract group permits one not to worry about this discrepancy.