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  2. Seven-dimensional space - Wikipedia

    en.wikipedia.org/wiki/Seven-dimensional_space

    When n = 7, the set of all such locations is called 7-dimensional space. Often such a space is studied as a vector space , without any notion of distance. Seven-dimensional Euclidean space is seven-dimensional space equipped with a Euclidean metric , which is defined by the dot product .

  3. Intuitionism - Wikipedia

    en.wikipedia.org/wiki/Intuitionism

    The fundamental distinguishing characteristic of intuitionism is its interpretation of what it means for a mathematical statement to be true. In Brouwer's original intuitionism, the truth of a mathematical statement is a subjective claim: a mathematical statement corresponds to a mental construction, and a mathematician can assert the truth of a statement only by verifying the validity of that ...

  4. Logical intuition - Wikipedia

    en.wikipedia.org/wiki/Logical_intuition

    Logical Intuition, or mathematical intuition or rational intuition, is a series of instinctive foresight, know-how, and savviness often associated with the ability to perceive logical or mathematical truth—and the ability to solve mathematical challenges efficiently. [1]

  5. Module (mathematics) - Wikipedia

    en.wikipedia.org/wiki/Module_(mathematics)

    Modules of this type are called free and if R has invariant basis number (e.g. any commutative ring or field) the number n is then the rank of the free module. If M n (R) is the ring of n × n matrices over a ring R, M is an M n (R)-module, and e i is the n × n matrix with 1 in the (i, i)-entry (and zeros elsewhere), then e i M is an R-module ...

  6. Intuitionistic logic - Wikipedia

    en.wikipedia.org/wiki/Intuitionistic_logic

    Formalized intuitionistic logic was originally developed by Arend Heyting to provide a formal basis for L. E. J. Brouwer's programme of intuitionism. From a proof-theoretic perspective, Heyting’s calculus is a restriction of classical logic in which the law of excluded middle and double negation elimination have been removed. Excluded middle ...

  7. Genus (mathematics) - Wikipedia

    en.wikipedia.org/wiki/Genus_(mathematics)

    In layman's terms, the genus is the number of "holes" an object has ("holes" interpreted in the sense of doughnut holes; a hollow sphere would be considered as having zero holes in this sense). [3] A torus has 1 such hole, while a sphere has 0. The green surface pictured above has 2 holes of the relevant sort. For instance:

  8. Operation (mathematics) - Wikipedia

    en.wikipedia.org/wiki/Operation_(mathematics)

    An n-ary operation ω on a set X is a function ω: X n → X. The set X n is called the domain of the operation, the output set is called the codomain of the operation, and the fixed non-negative integer n (the number of operands) is called the arity of the operation. Thus a unary operation has arity one, and a binary operation has arity two.

  9. Lipschitz continuity - Wikipedia

    en.wikipedia.org/wiki/Lipschitz_continuity

    The smallest constant is sometimes called the (best) Lipschitz constant [4] of f or the dilation or dilatation [5]: p. 9, Definition 1.4.1 [6] [7] of f. If K = 1 the function is called a short map , and if 0 ≤ K < 1 and f maps a metric space to itself, the function is called a contraction .

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