09 May '05 04:37

Suppose two farmers (farmer A and B) are planting two separate infinitely long rows of seeds. They work side by side, planting the seeds at the same rate.

At the same time, two birds (birds A and B) are trying to make their lives difficult. Bird A is following farmer A and Bird A is eating every tenth seed that farmer A throws down. Meanwhile, Bird B is following Farmer B, and after every tenth seed Farmer B throws down, Bird B eats the first remaining seed in Farmer B's row.

Thus the farmers are planting at the same rate, and the birds are eating at the same rate.

However, when farmer A "finishes" his row, there are infinitely many seeds left that Bird A did not eat; on the other hand, when farmer B "finishes" his row, there will be no seeds left in his row, for bird B will eat every one eventually.

How can this be?

At the same time, two birds (birds A and B) are trying to make their lives difficult. Bird A is following farmer A and Bird A is eating every tenth seed that farmer A throws down. Meanwhile, Bird B is following Farmer B, and after every tenth seed Farmer B throws down, Bird B eats the first remaining seed in Farmer B's row.

Thus the farmers are planting at the same rate, and the birds are eating at the same rate.

However, when farmer A "finishes" his row, there are infinitely many seeds left that Bird A did not eat; on the other hand, when farmer B "finishes" his row, there will be no seeds left in his row, for bird B will eat every one eventually.

How can this be?