Hola Pasi, > > question posed by the paradox is: what is the sum of infinitely many > > infinitely small numbers (infinitesimals)? > > Actually the fallacy is that in Zeno we are only approaching the moment > of passing. In real life time doesn't slow down when you try to accomplish > something... :-) It is easy to reach time T and beyond. Well, I guess we should visit some of the web sites and see what they have to say, but I think I stated (and resolved) the issue correctly. That is, the reason it's a paradox is that two different methods of reasoning appear to lead to a contradictory conclusion. The first method is common sense and experience, which gives the answer you state above -- I can walk across a room. But Zeno says, "If I describe this problem mathematically, I come to the conclusion that it takes an infinite amount of time to cross the room/catch up to the turtle." So Zeno is challenging mathematics, not physical reality or philosophy, which is why the resolution to the paradox is to show that mathematics comes to the same conclusion as common sense. Historically, I think it took mathematics a while to develop enough to resolve the paradox. -Steve - This message was sent through the cbm-hackers mailing list. To unsubscribe: echo unsubscribe | mail cbm-hackers-request@dot.tcm.hut.fi.
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