tudwell writes:
It seems to me it must be infinite. If it's a finite number, then adding the one uninhabited planet to find the total number of planets would render a finite number, which is impossible given the premise of an infinite number of worlds.
This seems a little like the old problem of hilberts hotel..
In Hilberts hotel there are an infinite number of rooms,
So, a guest arrives and asks for a room
But he is told there are also an infinite number of guests,
His solution is to move the person in room one to room two, the person in room two to room three and so on, Then the newcomer moves into Room one.
It's kind of a work around for the problem of infinity.
There are also level of infinity, Alef-null, alef-one, Epsilon-zero, epsilon-one.... etc
This accounts for a situation where you have infinity within an infinity.
i.e. you break something down into an infinite number of smaller parts. you have infinity.
but the original object is one of an infinite number of parts in a bigger "object" another infinity so you need different levels of infinity.
It's early and I'm not doing a very good job at explaining this.
there is a very good book called "infinity and the mind" By Rudy Rucker, he also has one called "geometry, relativity and the fourth dimension" which kinda deals with similar topics.
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