Galileo’s Paradox of Infinity—Lectures on Infinity (lecture 6)

Galileo recognized that some infinite collections can be placed into one-to-one correspondence with a proper subcollection. How are we thus to make comparisons of size with the infinite?

Welcome to these Lectures on Infinity, my series of lectures exploring all my favorite paradoxes and conundrums, based on my book, The Book of Infinity.

In this instance, we shall consider Galileo’s paradox of infinity and the concept of equinumerosity for infinite collections.

• A transcript of this lecture is available.

• Find the lectures here on Infinitely More in the lectures-on-infinity tag.

• The lectures are appearing on YouTube.

• The whole lecture course is hosted at Ergo: Lectures on Infinity.

• This lecture is based on my essay Equinumerosity and Comparison of Size.

• The essay appears in my new book, The Book of Infinity.