Z

“We'll start with Zeno and the classical ideas of Aristotle and Archimedes, but eventually, we'll move through Galileo, and then we'll see Frege, and Dedekind, and Cantor, and the 20th century…” (Joel David Hamkins)

“I want to start with a classical thinker, Zeno of Elea, who made a very interesting argument. Namely, Zeno argued, this was in about 450 BC, and Zeno argued that all motion is impossible. You cannot…” (Joel David Hamkins)

“Zeno was walking from here to there, or he argued that it's not possible to walk from here to there, and I don't wanna do the Zeno paradox in the first manner that we had described it, but rather in…” (Joel David Hamkins)

“to this series of lectures on infinity. I wanna show you all my favorite conundrums and paradoxes of infinity. We're gonna see Zeno's paradox, and the paradox of supertasks, Galileo's paradox, the…” (Joel David Hamkins)

“features of this argument that I've just given. Namely, if you think about the Zermelo axiomatization of set theory that he provided first in 1904, but then more refined in 1908, Zermelo set theory…” (Joel David Hamkins)

“theory, or any of the standard axiomatizations of mathematics, then there must be programs, and in fact relatively small programs, that don't halt, but the theory cannot prove this. And so this calls…” (Joel David Hamkins)

“path, okay, that looks like this. This sort of winding zigzag path. So, on the first turn, the glutton will eat this chocolate. And then on the next turn, the” (Joel David Hamkins)