Craig Feinstein wrote: > > Let's say I have a drawer of an infinite number of identical socks at time zero. I take out one of the socks at time one. Then the contents of the drawer at time zero is identical to the contents of the drawer at time one, since all of the socks are identical and there are still an infinite number of them in the drawer at both times. But the contents of the drawer at time zero is also identical to the contents of the drawer at time one plus the sock that was taken out, since they are exactly the same material. So we have the equations: > > Contents of drawer at time 0 = Contents of drawer at time 1 > Contents of drawer at time 0 = (Contents of drawer at time 1) plus (sock taken out of drawer). > > Subtracting the equations, we get > > Nothing = sock taken out of drawer. > > This is false, so infinity cannot exist. > > How does modern mathematics resolve this paradox?
If alpha - 1 is defined to be that beta such that alpha = beta + 1, then aleph_0 - 1 = aleph_0.
-- When a true genius appears in the world, you may know him by this sign, that the dunces are all in confederacy against him. Jonathan Swift: Thoughts on Various Subjects, Moral and Diverting