In article <earle.jones-405E2F.firstname.lastname@example.org>, Earle Jones <email@example.com> wrote:
> In article <firstname.lastname@example.org>, > Craig Feinstein <email@example.com> 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? > > * > Let k = the number of numbers. > Let q = the number of even numbers. > > Which is larger, k or q?
Depends what you mean by "larger".
On of them is a proper superset of the other and as such is larger in that one sense, but they biject each with the other so in a different sense they are of the same size.
Similarly when comparing physical objects, the one which is greater by weight may well be smaller by volume.
So when comparing objects with more than one measurable quality, one must specify which quality is the relevant one. --