[Ramius]

But of course that is absurd, since APPROACHING infinity is not the same as infinity. 10 ^^ x is a very large number, depending on x, but it is still not infinite.

No... I think it's infinite. Unless at some point nothing can ever get any smaller... which of course never happens. The rabbit can always go halfway, forever. He never reaches the carrot.

[MontaniSemperLiberi]

Formally, “In the limit of x approaching infinity, 10**x approaches infinity.”

I know it seems silly but there was a philosophical argument 200+ years ago on if man could understand infinity. It was decided that man can understand approaching infinity but not infinity.

[IronJack]

You’re right. It takes forever for the rabbit to reach the carrot. But the distance to the carrot is finite. It can be measured. The same is true of the length of a shoreline. We KNOW it can be measured, but if we keep defining it more and more granularly, eventually it becomes infinite.

[tet68]

Considering an expanding universe it’s true.

I remember another example, a boy and a girl are on
opposite sides of the room, they half the distance between
them each time, they never touch but are “close enough
for all practical purposes”.