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In mathematics, a set is a collection of different [1] things; [2] [3] [4] these things are called elements or members of the set and are typically mathematical objects of any kind: numbers, symbols, points in space, lines, other geometrical shapes, variables, or even other sets. [5] A set may have a finite number of elements or be an infinite set.
Reproducibility, closely related to replicability and repeatability, is a major principle underpinning the scientific method.For the findings of a study to be reproducible means that results obtained by an experiment or an observational study or in a statistical analysis of a data set should be achieved again with a high degree of reliability when the study is replicated.
Identity element. In mathematics, an identity element or neutral element of a binary operation is an element that leaves unchanged every element when the operation is applied. [1] [2] For example, 0 is an identity element of the addition of real numbers. This concept is used in algebraic structures such as groups and rings.
Although the theory is that the similarity of elements facilitates transfer, there is a challenge in identifying which specific elements had an effect on the learner at the time of learning. Factors that can affect transfer include: Context and degree of original learning: how well the learner acquired the knowledge.
A proof by double counting. A combinatorial identity is proven by counting the number of elements of some carefully chosen set in two different ways to obtain the different expressions in the identity. Since those expressions count the same objects, they must be equal to each other and thus the identity is established. A bijective proof.
Run-length encoding ( RLE) is a form of lossless data compression in which runs of data (consecutive occurrences of the same data value) are stored as a single occurrence of that data value and a count of its consecutive occurrences, rather than as the original run. As an imaginary example of the concept, when encoding an image built up from ...
Set (abstract data type) In computer science, a set is an abstract data type that can store unique values, without any particular order. It is a computer implementation of the mathematical concept of a finite set. Unlike most other collection types, rather than retrieving a specific element from a set, one typically tests a value for membership ...
In set theory, the union (denoted by ∪) of a collection of sets is the set of all elements in the collection. [1] It is one of the fundamental operations through which sets can be combined and related to each other. A nullary union refers to a union of zero ( ) sets and it is by definition equal to the empty set.