Imagine a cookie. It's one of those giant pie-plate cookies from the mall.
Cookie Monster comes over and eats half the cookie!
Then Cookie Monster eats half of what's left. Then again and again...and he keeps eating and eating!
The piece of cookie remaining gets smaller and smaller. At some point Cookie Monster runs off to find a new cookie flavor. He leaves some portion of the cookie behind.
Maybe only 1⁄4096th of a cookie, but that's still a couple of crumbs.