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1. Irrational Numbers 2. Sequences 3. Series 4. Power Series 5. The Exponential Binomial and Logarithmic Series
"Irrational Numbers and Their Representation by Sequences and Series" by "Henry Manning", first published in 1906, is a classic mathematical work exploring the nature and definition of "irrational numbers". Manning explains how numbers that cannot be expressed as fractions can instead be represented through "sequences" and "infinite series", giving them a rigorous foundation in mathematical analysis. The book introduces key ideas such as limits, convergence, and the construction of irrational numbers as limits of rational sequences. Manning also discusses important series, including the binomial and exponential series, showing how infinite processes help define numbers beyond rational representation. His clear and methodical approach made the book valuable for both students and teachers interested in understanding the logic behind real numbers. Even over a century later, "Irrational Numbers and Their Representation by Sequences and Series" remains relevant as a foundational text in mathematical theory. By combining clarity with rigor, "Henry Manning" provided an accessible yet precise explanation of how infinite sequences and series form the basis for understanding irrational quantities—making the book a timeless reference in the study of number systems.
Title: Irrational Numbers and Their Representation by Henry Manning Publisher: J. Wiley & sons Year: 1906 Pages: 156 Type: PDF Language: English ISBN-10 #: 1437186599 ISBN-13 #: 978-1112278235 License: Public Domain Work Amazon: Amazon
The author Henry Parker Manning (1859–1956) was an American mathematician and professor at "Brown University", known for his clear and logical approach to "mathematical analysis". He dedicated his career to making complex mathematical ideas understandable for students and educators. Manning is best known for his 1906 book, "Irrational Numbers and Their Representation by Sequences and Series", which explains how "irrational numbers" can be represented using sequences and infinite series. His precise and accessible writing style made lasting contributions to mathematics education and foundational theory.
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