The mathematics department at university held a raffle. The tickets were a little pricey at $10 each, but the prize was tantalizing: an infinite amount of money paid to the winner for an infinite amount of time. With such a prize on the line, the tickets sold like hotcakes, and the department soon raised thousands of dollars.
When the winner was announced, he gleefully came down to the department office to claim his prize. He found the department head, and asked that he receive his winnings. The department head congratulated the man, and happily pulled out a $1 bill and handed it to the winner.
“What’s this?” demanded the winner. “You promised me an infinite amount of money over an infinite amount of time!”
“Oh, yes, this is just the first installment,” replied the mathematican happily. “Next week you’ll get 1/2 a dollar, and the week after that 1/3, and the week after that 1/4…”