"Hey, the horizontal displacement of that pendulum is decaying with time!"
"No, it is obviously oscillating. You must be imagining things."

Question: How many times does the earth make a complete rotation about its own axis in the time it takes to orbit the sun? Round off to the nearest integer. (Think carefully! Try not to check any sources.)

The wonders of integration:

If your download speed decreases the moment you start downloading, such that your download speed is inversely proportional to time elapsed since the start of the download, you will ALWAYS be able to finish your download in a finite amount of time.

Suppose you have a tall glass. Its inner diameter decreases with depth, such that the inner diameter is inversely proportional to the depth. The inner diameter at the end of the tall glass is of a finite diameter, and extends infinitely downwards. This tall glass can hold a finite volume of water, but has infinite cross sectional area.