Mathematics: A Very Short Introduction (Very Short Introductions) by Gowers Timothy

Author:Gowers, Timothy [Gowers, Timothy]
Language: eng
Format: mobi, epub
Publisher: Oxford University Press
Published: 2002-08-21T16:00:00+00:00

Another way of putting it, which is perhaps clearer, is this. If a curved shape has an area of exactly 12 square centimetres, and I am required to demonstrate this using a grid of squares, then my task is impossible – I would need infinitely many of them. If, however, you give me any number other than 12, such as 11.9, say, then I can use a grid of squares to prove conclusively that the area of the shape is not that number: all I have to do is choose a grid fine enough for the area left out to be less than 0.1 square centimetres. In other words, I can do without infinity if, instead of proving that the area is 12, I settle for proving that it isn’t anything else. The area of the shape is the one number I cannot disprove.

Download

Copyright Disclaimer:
This site does not store any files on its server. We only index and link to content provided by other sites. Please contact the content providers to delete copyright contents if any and email us, we'll remove relevant links or contents immediately.