The Biggest Number in the World: A Journey to the Edge of Mathematics by David Darling

Author:David Darling [Darling, David]
Language: eng
Format: epub
ISBN: 9780861543052
Google: 652azgEACAAJ
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Publisher: Oneworld Publications
Published: 2022-03-10T18:36:55+00:00

In terms of Conway’s chained-arrow notation, the Ackermann–Péter function is equivalent to the three-element chain:

A(m, n) = (2 → (n + 3) → (m – 2)) – 3

in which, again, the 2 appears as the first element. Like the original Ackermann function, Conway’s chained arrows are not binary in nature. In particular, when three or more numbers are joined by arrows the arrows don’t act separately. Instead the whole chain has to be considered as a unit.

The Ackermann and other related non-primitive recursive functions are the jumping-off point for more developments in the use of specially crafted functions for reaching numbers at the edge of the observable universe of maths. But to understand these developments we need to delve further into computability theory and explore the limits of what it’s possible, even in theory, to compute.

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