TITLE: Infinite sets don't exist!?
QUESTION [78 upvotes]: Has anyone read this article?
This accomplished mathematician gives his opinion on why he doesn't think infinite sets exist, and claims that axioms are nonsense. I don't disagree with his arguments, but with my limited knowledge of axiomatic set theory and logic, I am unable to take sides. Would someone be so kind as to enlighten me on why his arguments are/aren't correct? Thanks

REPLY [6 votes]: Without taking a stand one way or another on the author's philosophical and pedagogical claims, I would like to correct him on one small point. When he writes (mockingly)

it surely is possible to dissect a solid unit ball into five pieces, and rearrange them to form a solid ball of radius two.

he seems to be misstating a result of Raphael M. Robinson related to the Banach-Tarski paradox. The correct statement:

It is possible to dissect a solid unit ball into five pieces, and rearrange them to form two solid unit balls.

It is also possible to dissect a solid unit ball into some finite number 
$N$ of pieces and rearrange them to form a solid ball of radius two, and I don't know what's the smallest $N$ that works, but I'm pretty sure it's bigger than $5.$