I'm listening to this, ... I don't understand the problem: I am personally quite happy with the idea of "finite but unbounded" which is something I intuitively grasped at about the age of five when I was taught how you could always add one to a number and get the next one, and you didn't need to invent any new names for bigger numbers as long as you were happy writing them as a formula (finite but unbounded in length) d_1 + 10 d_2 + 100 d_3 + 1000 d4 + ... In just five steps you already have 10,000 digit numbers, so in 10,000 steps, well, you get the idea, right? He's done several videos on this, some in conversation with other mathematicians and computer scientists, for example, here's one he did in September 2014 with James Franklin (see Infinity's end: Time to ditch the never-ending story? ) Norman is a bit of an extremist. For example, of this finite (and rather small number, relatively speaking) which he wrote on his whiteboard ( 11:53 ), he sta...