The Real Numbers: An Introduction to Set Theory and Analysis by John Stillwell PDF

By John Stillwell

whereas so much texts on genuine research are content material to imagine the true numbers, or to regard them purely in brief, this article makes a major learn of the true quantity method and the problems it brings to mild. research wishes the true numbers to version the road, and to aid the strategies of continuity and degree. yet those possible basic necessities bring about deep problems with set theory—uncountability, the axiom of selection, and massive cardinals. in reality, nearly the entire recommendations of countless set concept are wanted for a formal realizing of the true numbers, and as a result of research itself.By concentrating on the set-theoretic features of study, this article makes the easiest of 2 worlds: it combines a down-to-earth creation to set concept with an exposition of the essence of analysis—the examine of limitless tactics at the genuine numbers. it truly is meant for senior undergraduates, however it can be beautiful to graduate scholars mathematicians who, previously, were content material to 'assume' the genuine numbers. Its must haves are calculus and uncomplicated mathematics.Mathematical historical past is woven into the textual content, explaining how the thoughts of actual quantity and infinity constructed to fulfill the wishes of study from precedent days to the past due 20th century. This wealthy presentation of historical past, besides a heritage of proofs, examples, workouts, and explanatory comments, may also help inspire the reader. the fabric lined contains vintage themes from either set thought and genuine research classes, equivalent to countable and uncountable sets,  countable ordinals, the continuum challenge, the Cantor–Schröder–Bernstein theorem, non-stop features, uniform convergence, Zorn's lemma, Borel units, Baire capabilities, Lebesgue degree, and Riemann integrable functions.

Show description

Read Online or Download The Real Numbers: An Introduction to Set Theory and Analysis (Undergraduate Texts in Mathematics) PDF

Similar logic books

The Real Numbers: An Introduction to Set Theory and Analysis by John Stillwell PDF

Whereas so much texts on actual research are content material to imagine the genuine numbers, or to regard them purely in short, this article makes a significant examine of the true quantity approach and the problems it brings to gentle. research wishes the genuine numbers to version the road, and to help the strategies of continuity and degree.

Download e-book for iPad: The Unknown as an Engine for Science: An Essay on the by Hans J. Pirner,William D. Brewer

This ebook explores the boundaries of our wisdom. the writer exhibits how uncertainty and indefiniteness not just outline the borders confining our realizing, yet how they feed into the method of discovery and aid to beat back those borders. beginning with physics the writer collects examples from economics, neurophysiology, heritage, ecology and philosophy.

Introduction to Coalgebra: Towards Mathematics of States and - download pdf or read online

The world of coalgebra has emerged inside theoretical laptop technological know-how with a unifying declare: to be the math of computational dynamics. It combines principles from the idea of dynamical platforms and from the speculation of state-based computation. even if nonetheless in its infancy, it's an energetic zone of analysis that generates large curiosity.

New PDF release: Exploring Mathematics: An Engaging Introduction to Proof

Exploring arithmetic provides scholars adventure with doing arithmetic - interrogating mathematical claims, exploring definitions, forming conjectures, making an attempt proofs, and providing effects - and engages them with examples, workouts, and initiatives that pique their curiosity. Written with a minimum variety of pre-requisites, this article can be utilized through students of their first and moment years of research, and via self reliant readers who wish an obtainable creation to theoretical arithmetic.

Additional resources for The Real Numbers: An Introduction to Set Theory and Analysis (Undergraduate Texts in Mathematics)

Example text

Download PDF sample

The Real Numbers: An Introduction to Set Theory and Analysis (Undergraduate Texts in Mathematics) by John Stillwell


by Edward
4.0

Rated 4.82 of 5 – based on 37 votes