> If we assume that the room is infinitely large (and compared to the size of the beaker it might as well be) and at a constant temperature of 20ºC, then the beaker will gradually rise in temperature back to 20ºC (the mathematician in me now points out that it will only reach that temperature after an infinite time, but the engineer in me says "Who cares? It'll be 99.9% of the way there in a finite amount of time, and that's good enough")

Okay, NOW I remember what I wanted to ask about this particular bit of math. :-)

I've think I've heard it's a standard assumption to claim a rate-limiting process will eventually "get 99.9% of the way where it's supposed to go in a finite amount of time, and so 'that's good enough.'" Engineers are the ones who make this claim about real-world parameters; I've never really heard any other discipline talk in this way. Is this a joke which is commonly taught in engineering school? For what situations? I'm pretty sure the assumption doesn't hold for the contents of a beaker -- or a cup of coffee -- eventually achieving thermal homeostasis with its ambient environment (i.e. thermal equilibrium).

Wolf "sounds like a modern variant of Zeno's Paradox involving the neverending race between the tortoise and Achilles" spirit