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In set theory, -induction, also called epsilon-induction or set-induction, is a principle that can be used to prove that all sets satisfy a given property. Considered as an axiomatic principle, it is called the axiom schema of set induction. The principle implies transfinite induction and recursion.
Bourbaki also defines an inductive set to be a partially ordered set that satisfies the hypothesis of Zorn's lemma when nonempty.. In descriptive set theory, an inductive set of real numbers (or more generally, an inductive subset of a Polish space) is one that can be defined as the least fixed point of a monotone operation definable by a positive Σ 1 n formula, for some natural number n ...
James Frederick Bonk (February 6, 1931 – March 15, 2013) was an American university professor noted for eschewing a research career in favor of teaching introductory chemistry courses for over 50 years, primarily at Duke University. [1] He did, however, also teach advanced and graduate courses, and wrote his own textbooks and laboratory manuals.
Chemistry education (or chemical education) is the study of teaching and learning chemistry. It is one subset of STEM education or discipline-based education research (DBER). [ 1 ] Topics in chemistry education include understanding how students learn chemistry and determining the most efficient methods to teach chemistry.
Inductive reasoning is any of various methods of reasoning in which broad generalizations or principles are derived from a body of observations. [1] [2] Inductive reasoning is in contrast to deductive reasoning (such as mathematical induction), where the conclusion of a deductive argument is certain, given the premises are correct; in contrast, the truth of the conclusion of an inductive ...
It is noted that no law of science can be considered mere inductive generalization of facts because each law does not exist in isolation. [8] This is for, instance, demonstrated by thinkers such as John Stuart Mill, who maintained that inductionism is the initial act in the formulation of a general law using the deductive approaches to science. [9]
Type theory was created to avoid a paradox in a mathematical equation [which?] based on naive set theory and formal logic. Russell's paradox (first described in Gottlob Frege's The Foundations of Arithmetic) is that, without proper axioms, it is possible to define the set of all sets that are not members of themselves; this set both contains itself and does not contain itself.
The inductive effect is the transmission of charge through covalent bonds and Bent's rule provides a mechanism for such results via differences in hybridisation. In the table below, [ 26 ] as the groups bonded to the central carbon become more electronegative, the central carbon becomes more electron-withdrawing as measured by the polar ...