OT - Physics Question on Anti-Matter

[douglas]

There's a whole class of infinities described as "countably infinite" that are all equivalent in size and (among other things) have the property that any two such infinities can be combined to make another infinity that is also countably infinite. The number of rooms in the hotel, the number of current occupants, and the number of frat boys are all countably infinite and can therefore be combined without changing anything. If a fraternity with one member for each irrational number showed up, however, the hotel would be in trouble because that particular set is not countably infinite. No matter what scheme you came up with for assigning people to rooms, you would always have an infinite number still waiting.

Note: A set is countably infinite if and only if it is possible to assign each and every member of the set to a corresponding member of another countably infinite set (the set of all integers is declared to have this property by fiat so you have a base to work with) so that each and every member of both sets has a corresponding member in the other. Put another way, if it's possible to come up with a scheme for labelling each and every item with a different whole number without skipping any numbers, then the set is countably infinite.

On a side note, the set of rational numbers is also countably infinite, but I'll leave figuring out a proof for it to everyone else. I know of one and will post it if enough people ask, but for now I'll leave it as a puzzle.

[PvK]

If there are an infitite number of rooms, it'll probably take you an infinite amount of time to get them to change rooms. Oh NOOOooo...!

[douglas]

No no, everyone changes rooms simultaneously and they use special teleporters that can take such things as "double my room number" as the destination so you don't even have to worry about how long it's going to take the people with room numbers with a trillion digits to enter them.

[Suicide Junkie]

Also, the fire code requires an instantaneous FTL intercom.

[narf poit chez BOOM]

Er...No. All you've done is introduced an infinite 'ripple' as people move from room to room. You havn't made more room; you've simply...

...Look, this should explain it. Infinity is not a number. It can, however, be a ratio.

Suppose you have a thirty foot fence and an apple every six inches.

You therefore have 15 epples, thirty feet of fence and 1 apple per 6 inches of fence. 1/6.

Supposing then that an infinite being, for no particular reason, makes the fence inifinitly long and makes sure there's an apple every six inches.

You then have an infinite amount of apples, an infinite amount of fence and a ratio of 1/6 of apples and inches of fence.

Supposing, then, that the infinite being doubled the number of apples, again spacing them evenly. You then have 2/6 or 1/3 of apples and inches.

The ratio of rooms to people is 1/1.

Add in another infinity of people and the ratio of rooms to people is 1/2.

However, as there will *always be more rooms opening up, you've disguised that. However, that 'ripple' is going to go on to infinity - And there will always be one displaced person.

* Unless all this is done in no time at all.

[Suicide Junkie]

Everybody moves at the same time. No ripple, just a quick and simultaneous changing of location.

And yes, practical physical limitations have to be ignored. That's why it is a thought experiment and not a fantastic way to make an infinite amount of profit in just one day.

The best part of course, would be that even though the taxman would take an infinite amount of money, you'd still have an infintite amount left (unless the tax rate happens to be 100%).

[narf poit chez BOOM]

The thing you're ignoring is that, while there would always be a room opening up, the room the person is moving into is occupied. The best you could get is to always have someone in transit.

This, of course, may not hold true if action is taken by a being greater than infinite, which would be the only theoretical way to have everyone move at the same time.

[aegisx]

I think Red Dwarf says it all. There was an episode where Dave (who had been in chyo for millions of years) got a message from earth about his bank account. Apparently he has 13 cents or something in there when he left, it now accounts for pretty much all of the money due to the interest. However, he left a lightbulb on in his apartment, so his bill accounts of all of that. I think that is how it went

[douglas]

narf poit chez BOOM said:
The thing you're ignoring is that, while there would always be a room opening up, the room the person is moving into is occupied. The best you could get is to always have someone in transit.

That would be true if we were moving people one at a time, but we're not. The hotel's intercom brings the room change announcement to every room simultaneously, and each person moves himself, so all moves are accomplished all at once. When the manager tells everyone to move to the room with double their current room number, person 2 doesn't show up at room 4 and then have to wait for person 4 to leave, person 4 is already out. As is person 8, 16, 32, 64, 128, and so on down the line. Here's how it works at Hotel Infinity:

Step 1: Manager gets on the intercom and tells everyone to move to the room with double his current room number. The intercom relays this message to everyone simultaneously, so all infinity residents are notified in as little time as it takes to say the announcement once.
Step 2: All occupants pack up and move themselves and their belongings into the hall. Every room is now empty.
Step 3: Each occupant steps into the teleporter across the hall and gives "double my previous room number" as the destination. All even numbered rooms are now occupied, but the odd numbered rooms are still empty.

After these steps are completed, in the finite time required for a single person to change rooms, every previous resident has a new room, no one had to be tossed out, and everyone is finished moving into his or her new room. The Hotel contains exactly as many people as it did before, but now every odd numbered room is empty, giving enough room for the entire fraternity of infinite odd-numbered people to move in.

[PvK]

Well if you want infinite money, just become a bank and start charging compound interest...