[math-fun] Another infinite joke...

You're visiting your friend at her apartment, and start discussing mathematical paradoxes. "Suppose," you say, "that you flip the light switch on, then after a second you flip it off.  Then, after a further half-second you flip it on again, and after another quarter-second flip it off.  Keep doing this on-off-on-off for shorter and shorter intervals, halving their length each time.  After two seconds you will have flipped the switch an infinite number of times and you stop.  Is the light on or off?" "Oh, I couldn't do that," she says. "But suppose you could," you counter. "But I couldn't!" she insists.  "I'd have to call building maintenance for that.  That's a super-task!"