This came about on a test today (we have handed it in) and it just got to me. I didn't think it was hard until my teacher made an outrageous claim. Here goes nothin: A hammer strikes a nail, and the nail goes in .8 cm. On the second strike, it will go in .7 cm. It is a geometric sequence. How far will the nail go in an infinite amount of hammer strikes? Now, I said infinitely far. My teacher said that we should assume the nail could keep going even after it's flush with the wood. He also declared that there was an exact and real number that it would be (the answer). He compared it to the example he used earlier in the year: "I am walking towards that door. I will go halfway there each time. I won't ever reach the door." Now, I don't think that really applies here. My reasoning for saying 'infinitely far' is that each time, it goes further, therefore in infinitely many strike, it will go infinitely far.