Q&A: Mathematics and That Sort of Thing
Mathematics and That Sort of Thing
Question
Hi Michi, how are you? I have two questions.
1) I don’t have broad knowledge of mathematics at all, and I want to study and understand it—are there any books you recommend learning from?
2) Is the solution to the paradox of Achilles and the tortoise that in the end the distance is finite and not infinite, so maybe you can’t divide something finite into infinitely many parts? That’s כמובן just my speculation; as I said, I don’t have any knowledge of mathematics (beyond high school matriculation).
Answer
1. It’s hard to learn mathematics from books. The vast majority of people will need a lecturer or some kind of help. There is of course popular literature, but I’m not familiar with it.
2. Indeed, the “paradoxical” description is nothing more than dividing a finite span of time into infinitely many slices (that is a convergent infinite series), and therefore there is no paradox. After that amount of time passes, Achilles will catch up to the tortoise.
Books from the Open University are very suitable for self-study. I recommend Calculus 1 by Gil Alon and Set Theory by Berger. They’re suitable for a beginning reader.