i don't think infinity exists like i think a lot of people in this thread intend it, i think infinity isn't that which has no bounds but that which we can't give bounds. That is to say, and my latin's very bad so excuse me on this, infinite comes from infinitus in latin, which i think is actually the past participle of a transitive verb, which means the action of "ending" isn't attributed to the thing described but to something else which bestowed the state on the object. in fact, i lived abroad for a while in italy and i swear i heard people say their homework was "infinito" once or twice... anyway i like the more practical view of infinity, that is, it might as well be infinite cuz it's so big. i actually had a rather interesting discussion with my physics professor concerning the nature of time and we decided that, in accordance with aristotle or plato i believe, that time really only exists as a dimensionless ratio among velocities (actually accelerations and actually all higher order derivatives of displacement, but for all intensive purposes it doesn't matter) that is only space and matter exist, not time. another one of our discussions (and we have had a fair number of discussions in our day... we're really a couple of bums) actually did lead us to conclude that the universe (note i don't say time because we had previously agreed that time is a secondary property of mass and space) is cyclic and happens the same way every time - in a desperate attempt to explain entropy and conservation laws and stuff. just to let you know how serious we were, it involved dual universes with reversed time in 4 spacial dimensions, where the universe was a shape only possible in the four dimensions but when brought to three was actually kinda folded back over itself... yeah anyway i think this is a fascinating topic and don't mean to intrude or anything, i just think the real question shouldn't be "what is infinity" but "what is it about the idea of infinity that makes it something we should concern ourselves with". i mean, i could concoct a completely fantastic other concept just as airy and ill-defined as infinity, and discuss that, but to what end and to serve what higher purpose? philosophy is good, but i think there can be too much of a good thing. another question that arose with my physics prof that hasn't been mentioned but which i think directly applies: ask the same thing about zero. what is nothing? define that, and infinity is the opposite.