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Titlebook: In Search of Infinity; N. Ya. Vilenkin Book 1995 Springer Science+Business Media New York 1995 Finite.clsmbc.function.mathematics.physics

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发表于 2025-3-21 17:09:46 | 显示全部楼层 |阅读模式
书目名称In Search of Infinity
编辑N. Ya. Vilenkin
视频video
图书封面Titlebook: In Search of Infinity;  N. Ya. Vilenkin Book 1995 Springer Science+Business Media New York 1995 Finite.clsmbc.function.mathematics.physics
描述The concept of infinity is one of the most important, and at the same time, one of the most mysterious concepts of science. Already in antiquity many philosophers and mathematicians pondered over its contradictory nature. In mathematics, the contradictions connected with infinity intensified after the creation, at the end of the 19th century, of the theory of infinite sets and the subsequent discovery, soon after, of paradoxes in this theory. At the time, many scientists ignored the paradoxes and used set theory extensively in their work, while others subjected set-theoretic methods in mathematics to harsh criticism. The debate intensified when a group of French mathematicians, who wrote under the pseudonym of Nicolas Bourbaki, tried to erect the whole edifice of mathematics on the single notion of a set. Some mathematicians greeted this attempt enthusiastically while others regarded it as an unnecessary formalization, an attempt to tear mathematics away from life-giving practical applications that sustain it. These differences notwithstanding, Bourbaki has had a significant influence on the evolution of mathematics in the twentieth century. In this book we try to tell the reader h
出版日期Book 1995
关键词Finite; clsmbc; function; mathematics; physics
版次1
doihttps://doi.org/10.1007/978-1-4612-0837-2
isbn_softcover978-1-4612-6915-1
isbn_ebook978-1-4612-0837-2
copyrightSpringer Science+Business Media New York 1995
The information of publication is updating

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发表于 2025-3-21 23:21:16 | 显示全部楼层
The mysteries of infinite sets,Pythagoras, Zeno, Plato, and Aristotle all discussed the one and the many. One Pythagorean defined a (natural) number as a collection of units, and in Book VII of the . Euclid writes that “Number is a collection consisting of units” (in ancient Greek mathematics one was not regarded as a number).
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https://doi.org/10.1007/978-1-4612-0837-2Finite; clsmbc; function; mathematics; physics
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Conclusion, to tame it and use it to apprehend reality. First there were the myths. Then came the first scientific quests of Pythagoras, Zeno and Aristotle. By now mankind has attained such impressive achievements as the modern cosmological theories, the intricate constructions of mathematical analysis, and the theory of infinite-dimensional spaces.
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In search of the absolute,Speaking of the role of intuition and logic in mathematics, he said that mathematics finds in set theory an absolutely permanent and reliable foundation, and now all that remains are the natural numbers and finite or infinite systems of such numbers. In his view, mathematics had become completely arithmetized and, finally, absolutely rigorous.
发表于 2025-3-22 23:46:50 | 显示全部楼层
Book 1995philosophers and mathematicians pondered over its contradictory nature. In mathematics, the contradictions connected with infinity intensified after the creation, at the end of the 19th century, of the theory of infinite sets and the subsequent discovery, soon after, of paradoxes in this theory. At
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