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More generally, one may define upper bound and least upper bound for any subset of a partially ordered set X, with “real number” replaced by “element of X ”. In this case, we say that X has the least-upper-bound property if every non-empty subset of X with an upper bound has a least upper bound in X.
CK-12 FlexBooks are designed to facilitate conformance to national and United States and individual state textbook standards. CK-12 FlexBooks are licensed under a Creative Commons BY-NC-SA license. CK-12 FlexBooks are free to use online and offer formats suitable for use on portable personal reading devices and computers – both online and ...
The solution to this particular problem is given by the binomial coefficient (+), which is the number of subsets of size k − 1 that can be formed from a set of size n + k − 1. If, for example, there are two balls and three bins, then the number of ways of placing the balls is ( 2 + 3 − 1 3 − 1 ) = ( 4 2 ) = 6 {\displaystyle {\tbinom {2 ...
Bloom's taxonomy is a framework for categorizing educational goals, developed by a committee of educators chaired by Benjamin Bloom in 1956. It was first introduced in the publication Taxonomy of Educational Objectives: The Classification of Educational Goals.
The assumption that solution properties are independent of nature of solute particles is exact only for ideal solutions, which are solutions that exhibit thermodynamic properties analogous to those of an ideal gas, and is approximate for dilute real solutions. In other words, colligative properties are a set of solution properties that can be ...
Chemistry is the scientific study of the properties and behavior of matter. [1] It is a physical science within the natural sciences that studies the chemical elements that make up matter and compounds made of atoms, molecules and ions: their composition, structure, properties, behavior and the changes they undergo during reactions with other substances.
Trigonometry (from Ancient Greek τρίγωνον (trígōnon) 'triangle' and μέτρον (métron) 'measure') [1] is a branch of mathematics concerned with relationships between angles and side lengths of triangles.
The following outline is provided as a topical overview of science; the discipline of science is defined as both the systematic effort of acquiring knowledge through observation, experimentation and reasoning, and the body of knowledge thus acquired, the word "science" derives from the Latin word scientia meaning knowledge.