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Counting from Infinity: Yitang Zhang and the Twin Prime Conjecture [14] (2015) Taking the Long View: The Life of Shiing-shen Chern [15] (2010) I Want To Be A Mathematician: A Conversation with Paul Halmos [16] (2009) Julia Robinson and Hilbert's Tenth Problem [17] (2008) Hard Problems: The Road to the World's Toughest Math Contest [18] (2008)
Playing with Infinity presents a broad panorama of mathematics for a popular audience. It is divided into three parts, the first of which concerns counting, arithmetic, and connections from numbers to geometry both through visual proofs of results in arithmetic like the sum of finite arithmetic series, and in the other direction through counting problems for geometric objects like the ...
The aleph numbers differ from the infinity commonly found in algebra and calculus, in that the alephs measure the sizes of sets, while infinity is commonly defined either as an extreme limit of the real number line (applied to a function or sequence that "diverges to infinity" or "increases without bound"), or as an extreme point of the ...
The relevant section of Two New Sciences is excerpted below: [2]. Simplicio: Here a difficulty presents itself which appears to me insoluble.Since it is clear that we may have one line greater than another, each containing an infinite number of points, we are forced to admit that, within one and the same class, we may have something greater than infinity, because the infinity of points in the ...
From Zero to Infinity: What Makes Numbers Interesting is a book in popular mathematics and number theory by Constance Reid. It was originally published in 1955 by the Thomas Y. Crowell Company. [ 1 ] The fourth edition was published in 1992 by the Mathematical Association of America in their MAA Spectrum series.
Cantor said: The actual infinite was distinguished by three relations: first, as it is realized in the supreme perfection, in the completely independent, extra worldly existence, in Deo, where I call it absolute infinite or simply absolute; second to the extent that it is represented in the dependent, creatural world; third as it can be conceived in abstracto in thought as a mathematical ...
Infinity: Facts and Speculations of Science is a popular science book by theoretical physicist George Gamow, first published in 1947, but still (as of 2020) available in print and electronic formats. The book explores a wide range of fundamental concepts in mathematics and science, written at a level understandable by middle school students up ...
which increases without bound as n goes to infinity. Because the sequence of partial sums fails to converge to a finite limit, the series does not have a sum. Although the series seems at first sight not to have any meaningful value at all, it can be manipulated to yield a number of different mathematical results.