幽灵无理数

IF 0.4 4区数学 Q4 MATHEMATICS

American Mathematical Monthly Pub Date : 2023-03-29 DOI:10.1080/00029890.2023.2184619

Guojun Fang

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引用次数: 0

摘要

有理数可以用比率表示，而无理数不能。希帕索斯有时被认为发现了一个正方形的对角线长度是一个无理数。这是数学史上的一个重要发现。康托的对角线论证也加深了我们对有理数和无理数的认识。前者是可数无限的，后者是不可数无限的。它们在现实中也有不同的密度。我写了一首诗，描述了理性和非理性之间的区别，一些发现的历史，以及非理性的重要性和密度。

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Ghostly Irrational Numbers

Rational numbers can be expressed as ratios and irrational numbers cannot. Hippasus is sometimes credited with the discovery that the length of the diagonal of a square is an irrational number. This is an important discovery in the history of mathematics. Cantor’s diagonal argument also deepened our understanding of rational numbers and irrational numbers. The former are countably infinite and the latter are uncountably infinite. They also have distinct densities in the reals. I have written a poem which describes the differences between the rationals and the irrationals, a bit of history of the discovery, as well as the significance and the density of the irrationals.

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来源期刊

American Mathematical Monthly Mathematics-General Mathematics

CiteScore

0.80

自引率

20.00%

发文量

127

审稿时长

6-12 weeks

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