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Mon, Jul 07, 2008
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I've had a lot of spare time recently...
So there are an infinite number of numbers. And half of them are odd, and half of them are even.
So although there are an infinite number of even numbers, there are still only half as many as there are numbers. A smaller infinity.
Hence the reason why "infinity divided by infinity" is indeterminate. Is it a big or a small infinity you're using in each case?
The popular example is of somebody or other's postulate of a hotel with an infinite number of rooms, and a coach with an infinite number of people in it.
Nice and simple: An infinite number of guests for an infinite number of rooms. No problem.
Now every room is full.
Another infinite coach turns up. But every room is full. How do they find rooms?
They tell all the guests already in the hotel to move into the even-numbered rooms, and then the new coachload moves into the odd-numbered rooms. And now everyone has a room, and every room is full.
And then an INFINITE number of coaches arrives, each with an infinite number of people on board.
So they're all told to get out of their coaches, and then to get into just one of the coaches. And then the same solution as above can be used.
If you throw a ball to somebody an infinitely long way away, and wait for an infinitely long time, it will reach them. Right?
But what if there's a second person, infinitely far away from the first, in a direct line? That makes him doubly infinitely far away from you? No, just infinitely far away.
So if you throw that ball and wait for an infinitely long time... who will catch the ball?
As a concept, infinity is almost as tricky as zero, when you think about it.
So there are an infinite number of numbers. And half of them are odd, and half of them are even.
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Dominic can drive for another year! My little Fiesta survived its ordeal by MOT :).
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I last listened to:
The Offspring - She's Got Issues
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Submersible houseboat