Abstract Information

The rapper has his bling-bling, the professor has his or her trinkets - p, f, π - perhaps on a charm bracelet, more likely on black velvet, metaphorically, in the Museum at the End of the Universe. Speaking of museum displays, we all know that the almighty dollar of yore was backed by gold; and, as a fashion accessory, '$' too has its backing, referred to as 'street cred'; but what backs π, f, e and p? Nothing, save twenty centuries of double-think (carried on voluntarily, albeit only dazedly, in the Ivory Tower, no need for Orson Wells).

Have you ever wondered "Why not just write 1.4142, 1.6180, 2.7182 or 3.1415, as needed, instead of π, f, e or p, since we all know what those numbers signify already?" or "How can p be a static constant if its algorithm keeps spewing out digits, dynamically, for 33 to the octillionth power eternities?" If so, you've come to the right place. Here you will learn to appreciate the Dedekind Cut as a Solution in Search of a Problem, as we replace it by sundry algorithms that run - not to Infinity (a schoolyard concept) - but for Ever (a grown-up concept). By the way, the underlying idea is not my own; rather, this will be a series of arabesques and embroideries that follow Poundstone 1985 to its logical conclusion. (Not to worry - our assault leaves d, i and the ?-function unscathed; see Concluding Remarks.)

Continued