Xelebes wrote:
twoshots wrote:
Quote:
Just how are these infinite number of rooms numbered? Are we supposed to rely on transfinites for expressing that?
There is a room 1. For each room n there exists a room n+1 next door down the hall.
If a is next door down the hall from room n , and a is next door down the hall from room m also, then room m is actually room n.
Room 1 is up the hall from all other rooms.
If the person in room n coming out to party in the hallway causes the person in room n+1 to come out and party with them, and the person in room 1 comes out to throw a party in the hallway: then everyone comes out into the hallway to party.
Those rooms are not numbered! You can't label a room with a nebulous 'n' or 'm' and expect it to be numbered as any numbered item must have a label that is a real number not included in the transfinites. Any item that is numbered is finite, basically. Economics, my friend.
Let me explain this further. A catalogue is written of all the rooms - a catalogue must exist for any inventory of items for those who sell, elsewise it is untenable for God and St. Paul to manage. If the rooms are not numbered, there is no problem. But the rooms are numbered, meaning that the items are labeled and are part of the catalogue. If there is an infinite number, how is the infinite size of the room able to accommodate the infinite size of the label and the person within it?
If the hall exists, the label of the infinite room is
z. The size of the body,
k itself must be fit into it. The size of the room must be
z +
k, but it was assumed that the infinite room
z has the highest number, but the size of
z +
k is greater than it, unless we swing back down to negative infinites. We must also assume that the label has real size, that each number is meant to be legible. If the label is not legible, the room is not numbered.