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.