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Antoni Zygmund. Doctoral students. Peter Sarnak. Paul Joseph Cohen (April 2, 1934 – March 23, 2007) [1] was an American mathematician. He is best known for his proofs that the continuum hypothesis and the axiom of choice are independent from Zermelo–Fraenkel set theory, for which he was awarded a Fields Medal. [2]
The process of pattern recognition involves matching the information received with the information already stored in the brain. Making the connection between memories and information perceived is a step of pattern recognition called identification. Pattern recognition requires repetition of experience. Semantic memory, which is used implicitly ...
v. t. e. A Venn diagram is a widely used diagram style that shows the logical relation between sets, popularized by John Venn (1834–1923) in the 1880s. The diagrams are used to teach elementary set theory, and to illustrate simple set relationships in probability, logic, statistics, linguistics and computer science.
The need for cognition (NFC), in psychology, is a personality variable reflecting the extent to which individuals are inclined towards effortful cognitive activities. [1][2] Need for cognition has been variously defined as "a need to structure relevant situations in meaningful, integrated ways" and "a need to understand and make reasonable the ...
For Schema Theory in music, see Galant Schemata. In psychology and cognitive science, a schema (pl.: schemata or schemas) describes a pattern of thought or behavior that organizes categories of information and the relationships among them. [ 1 ][ 2 ] It can also be described as a mental structure of preconceived ideas, a framework representing ...
The continuum hypothesis states that the set of real numbers has minimal possible cardinality which is greater than the cardinality of the set of integers. That is, every set, S, of real numbers can either be mapped one-to-one into the integers or the real numbers can be mapped one-to-one into S.
Cohen's kappa measures the agreement between two raters who each classify N items into C mutually exclusive categories. The definition of is =, where p o is the relative observed agreement among raters, and p e is the hypothetical probability of chance agreement, using the observed data to calculate the probabilities of each observer randomly selecting each category.
Set theory is the branch of mathematical logic that studies sets, which can be informally described as collections of objects. Although objects of any kind can be collected into a set, set theory — as a branch of mathematics — is mostly concerned with those that are relevant to mathematics as a whole. The modern study of set theory was ...