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In number theory, a narcissistic number [1] [2] (also known as a pluperfect digital invariant (PPDI), [3] an Armstrong number [4] (after Michael F. Armstrong) [5] or a plus perfect number) [6] in a given number base is a number that is the sum of its own digits each raised to the power of the number of digits.
Given a number base , a natural number with digits is an automorphic number if is a fixed point of the polynomial function = over /, the ring of integers modulo.As the inverse limit of / is , the ring of -adic integers, automorphic numbers are used to find the numerical representations of the fixed points of () = over .
The Bulletin of Symbolic Logic, Volume 3, Number 2, June 1997. Barendregt, Hendrik Pieter, The Type Free Lambda Calculus pp1091–1132 of Handbook of Mathematical Logic, North-Holland (1977) ISBN 0-7204-2285-X; Cardone, Felice and Hindley, J. Roger, 2006. History of Lambda-calculus and Combinatory Logic Archived 2021-05-06 at the Wayback Machine.
In mathematical logic, a Gödel numbering is a function that assigns to each symbol and well-formed formula of some formal language a unique natural number, called its Gödel number. Kurt Gödel developed the concept for the proof of his incompleteness theorems .
The Y combinator is an implementation of a fixed-point combinator in lambda calculus. Fixed-point combinators may also be easily defined in other functional and imperative languages. The implementation in lambda calculus is more difficult due to limitations in lambda calculus. The fixed-point combinator may be used in a number of different areas:
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Mathematical induction can be informally illustrated by reference to the sequential effect of falling dominoes. [1] [2]Mathematical induction is a method for proving that a statement () is true for every natural number, that is, that the infinitely many cases (), (), (), (), … all hold.
The interesting number paradox is a humorous paradox which arises from the attempt to classify every natural number as either "interesting" or "uninteresting".