Ask HN: Does anyone know of any textbooks on infinity? | Hacker News Reader

Ask HN: Does anyone know of any textbooks on infinity?

I was just wondering if anyone knows any good textbooks on infinity.

I saw a post on HN (or maybe it was lobste.rs) a long time ago about a textbook on the same subject and I can't seem to find it anymore.

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One classic choice is "Infinity and the Mind" by Rudy Rucker, which explores infinity from both mathematical and philosophical perspectives.

For a more mathematical approach, "Understanding Infinity: The Mathematics of Infinite Processes" by A.C. Davis is a comprehensive option.

And if you're interested in the history of mathematical ideas, "The Mystery of the Aleph: Mathematics, the Kabbalah, and the Search for Infinity" by Amir D. Aczel is a fascinating read.

Here are a few popular science books:

  One Two Three . . . Infinity: Facts and Speculations of Science by George Gamow
  Infinity and the Mind: The Science and Philosophy of the Infinite by Rudy Rucker
  Yearning for the Impossible: The Surprising Truths of Mathematics by John Stillwell
  Roads to Infinity by John Stillwell

If you want actual textbooks then maybe pick up a set theory textbook like "Naive set theory" by Halmos.

Not a textbook, but Everything and More - A Compact History of Infinity by David Foster Wallace is a fun read about infinity. It’s technical but not quite as technical as a textbook that would be used in a college course. I have a PhD in math and I liked Everything and More a lot (but then again I also just love David Foster Wallace).

Another non-textbook: White Light by Rudy Rucker.

Any recommendation on good textbooks? Now I'm reading Eugenia Cheng's Beyond Infinity. I'm aware this is not textbook though, more like popular math book.

I’m not sure about textbooks specifically on infinity. As another comment mentions, the study of infinity generally falls under the math subject of set theory so a set theory textbook would be a mathematician’s definitive resource on infinity. I learned set theory from the book Elements of Set Theory by Herbert Enderton. I’d say that books alright, but would not give it my highest recommendation. It’s very dry and technical, and most of it’s not about infinity.

I've been writing one, but it still has no ending.

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