## asymmetric

Overview page. Subjects: Mathematics — Philosophy.

A relation R is asymmetric if when R*xy* it is not the case that R*yx*.

## 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.

## 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...

## 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.

## 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...

## 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...

## 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...

## 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...

## computable function

Overview page. Subjects: Computing — Philosophy.

A function

*f* : *X* → *Y*

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

## 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...