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asymmetric

Overview page. Subjects: Mathematics — Philosophy.

A relation R is asymmetric if when Rxy it is not the case that Ryx.

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asymptotic

Overview page. Subjects: Computing — Philosophy.

A line is asymptotic to a curve if the distance between the line and the curve tends to zero as the distance along the curve tends to infinity.

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Augustus De Morgan

Overview page. Subjects: Philosophy — Probability and Statistics.

(1806–71)

British mathematician and logician who was responsible for developing a more symbolic approach to algebra, and who played a considerable role in the beginnings of...

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axiom of choice

Overview page. Subjects: Philosophy — Mathematics.

States that for any set of mutually exclusive sets there is at least one set that contains exactly one element in common with each of the non-empty sets.

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Bernoulli theorem

Overview page. Subjects: Philosophy — Mathematics.

Title used for the ‘law of large numbers’ in probability theory, proved by Jakob Bernoulli (1654–1705). The theorem provides the best-known link between probability and the frequency of...

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Cantor's paradox

Overview page. Subjects: Philosophy — Mathematics.

Suppose there exists an infinite set A containing the largest possible number of elements. Cantor's Diagonal Theorem shows that its power set has more elements than A had. This proves there...

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Church's thesis

Overview page. Subjects: Philosophy — Computing.

The hypothesis, put forward by Alonzo Church in 1935, that any function on the natural numbers that can be computed by an algorithm can be defined by a formula of the lambda calculus. See...

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completeness

Overview page. Subjects: Computing — Philosophy.

The property or state of being logically or mathematically complete. In logic, an inference procedure is complete if it can derive every possible valid conclusion from the given axioms. A...

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computable function

Overview page. Subjects: Computing — Philosophy.

A function

f : XY

for which there exists an algorithm for evaluating f(x) for any element x in the domain X of f.

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condition, necessary/sufficient

Overview page. Subjects: Mathematics — Philosophy.

If p is a necessary condition of q, then q cannot be true unless p is true. If p is a sufficient condition of q, then given that p is true, q is so as well. Thus steering well is a...

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