Abstract
In this book we’ll always work within the so-called naïve set theory and completely avoid the axiomatic backgrounds. This choice has the advantage of leaving the reader free to pick his own preferred notions of ‘set’ and ‘element’, for instance ones suggested by conventional wisdom, or those learnt during undergraduate lectures on algebra, analysis and geometry. The only exception will concern the axiom of choice, whose content is less evident from the point of view of elementary logic, or to the layman.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
Russell’s paradox being the most widely known, see Sect. 8.1.
- 2.
Less frequently called ‘least-integer principle’.
- 3.
Known in Italy as Tartaglia’s triangle.
- 4.
The reader should be aware that this terminology is far from universal: some people call ‘countable’ what we defined as countably infinite, and use ‘at most countable’ to mean countable.
- 5.
Also these names are not universally accepted: some people call ‘ordering’ our total ordering, and ‘partial ordering’ our ordering. Poset (standing for ‘partially ordered set’) is another term for an ordered set.
References
Kelley, J.L.: General Topology. D. Van Nostrand Company, Toronto (1955)
Tourlakis, G.: Lectures in Logic and Set Theory, vol. 2. Cambridge University Press, Cambridge (2003)
Wagon, S.: The Banach–Tarski Paradox. Cambridge University Press, Cambridge (1993)
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2023 The Author(s), under exclusive license to Springer Nature Switzerland AG
About this chapter
Cite this chapter
Manetti, M. (2023). Sets. In: Topology. UNITEXT(), vol 153. Springer, Cham. https://doi.org/10.1007/978-3-031-32142-9_2
Download citation
DOI: https://doi.org/10.1007/978-3-031-32142-9_2
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-031-32141-2
Online ISBN: 978-3-031-32142-9
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)