A Brief History of Infinity: The Quest to Think the Unthinkable by Brian Clegg

Author:Brian Clegg [Clegg, Brian]
Language: eng
Format: epub
ISBN: 9781472107640
Amazon: B00AN2KHK8
Barnesnoble: B00AN2KHK8
Goodreads: 19369982
Publisher: Robinson
Published: 2015-07-01T05:00:00+00:00

all the way to infinity to get the value of the sum to be 2. We can say that the limit of the series is 2 as long as the difference between the sum of the series and 2 is smaller than a particular value (Weierstrass called this difference ε, the Greek letter epsilon) given any particular difference between the point the series has reached and 0 (this difference he called δ, delta). As Ian Stewart says in his survey of mathematics From Here to Infinity:

The introduction of potential versus actual infinity is a red herring: the whole problem can be formulated in purely finite terms.76

Weierstrass had not so much exorcised the ghost of the fluxion as photographed it and shown it to be someone dressed up in a sheet. Infinitesimals would remain these fake ghosts until the 1960s, when the possibilities of imagining the real thing were finally spotted. We will return to them in Chapter 16. But the considerations that were to make calculus respectable did not make the whole concept of infinity go away. The first steps that were taken by Galileo in his Discourse on Two New Sciences were to be given new life by another Italian.

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