Skip to main content

Sizes of Infinite Sets

  • Chapter
  • First Online:
A Readable Introduction to Real Mathematics

Abstract

How many natural numbers are there? How many even natural numbers are there? How many rational numbers are there? How many real numbers are there? How many points are there in the plane? How many sets of natural numbers are there? How many different circles are there in the plane? An answer to all these questions could simply be: there are an infinite number of them. But there are more precise answers that can be given; there are, in a sense that is explained and explored in this chapter, an infinite number of different size infinities.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

eBook
USD 19.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 29.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 29.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

Copyright information

© 2018 Springer Nature Switzerland AG

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Rosenthal, D., Rosenthal, D., Rosenthal, P. (2018). Sizes of Infinite Sets. In: A Readable Introduction to Real Mathematics. Undergraduate Texts in Mathematics. Springer, Cham. https://doi.org/10.1007/978-3-030-00632-7_10

Download citation

Publish with us

Policies and ethics