Indeed! Never underestimate the power of infinity! I'm bringing out my Gabriels Horn equation again.
For those of you who weren't in the Useful Facts thread:
Gabriels horn is the shape produced by revolving the graph 1/x around the x-axis from 1 to infinity. If you calculate its volume, you get a finite number... BUT if you calculate its surface area, you get infinity. So its can't hold enough paint to even paint its outside a infinitely small amount.
My calculus proof: (click to make bigger)
Another interesting concept that has been disputed before but pertains to infinite series:
0.99999999999999999...... = 1
Now I'm gonna get bitched at for this but think about it in this way. For two numbers to be 2 different numbers, there has to be a real number inbetween them right? There isn't any number that exists between .9999999... (repeating forever) and 1. So therefore they are the same number.
Another one of my favorite infinity related stories.
Its called Hotel Infinity and its a great read