I meant to write this up a while ago...

My wife and I traveled to Ecuador for two weeks and one thing we noticed in our guide book was La Capilla del Hombre ("Chapel of Man"), a Humanist chapel in the hills overlooking Quito.

A little history...

The Chapel was conceived by a man named Oswaldo Guayasamín. He was an Ecuadorean painter and sculptor who gained international recognition for his works depicting the emotions of the history of South America. They run the gamut from the pain of Spanish conquest, to exploitation by industries, to simple "working a living out of the earth to survive" dedication (whose name I can't quite think of at the moment), to the love and caring that radiate despite these things. It's been said that his work helped bring catharsis to many by exposing racism, poverty, and social injustice.

If I have an infinitely large bag and I take on a series of steps. Step 1 consists of adding 10 ping-pong balls, numbered 1 through 10, then removing ping-pong ball number 1. Step 2 consists of adding balls labeled 11 through 20, then removing ball #2. So, step n is adding balls 10n-9 through 10n, then taking out ball # n.

Q1: "After" an infinite number of steps, how many balls are in the bag?

Let us now say that step n consists of adding 10 balls, then removing 1 of them and none of them are labeled.

Q2: "After" an infinite number of steps, how many balls are in the bag?