48

46

the Tortoise and we choose to divide his course into a
first stage in which he goes to the place where the tortoise
was at first, a second stage in which he goes to the
place where the tortoise was at the end of the first
stage, a third stage in which he goes to the place where
the tortoise was at the end of the second stage, and so
on, the series of stages is endless. But nothing in
logic, or in fact, prevents Achilles from accomplishing
them all, since they are only possibilities. So then
there will be other ordinal numbers, after the first endless
series is gone through. And the first of these Cantor
denotes by ω then every ordinal number having
one next after it, the series runs
ω+1, ω+2, ω+3, ω+4, ω+5,
and after this endless series is accomplished then