On Mon, Oct 29, 2018 at 2:36 PM Philip Thrift <cloudver...@gmail.com> wrote:
>>Zeno thought it was obvious if you added an infinite number of nonzero >> lengths or nonzero times together you would always get something that was >> nfinite, and that is the foundation of his paradox; but with modern >> calculus we know that sometimes that isn't true, and when it isn't true >> calculus can tell you exactly what the FINITE length or finite time >> interval turns out to be. For example, the sum, of the infinite series: >> 1+1/4+1/9+1/16+1/25 + 1/36 + .... 1/N^2 is EXACTLY equal to (PI^2)/6. >> > > *> It is still a paradox* > It sure doesn't seem like a very good paradox to me. With calculus you can prove that 1/2 +1/4 + 1/8 + 1/16 + 1/25 + ....(1/2)^N is EXACTLY equal to 1, so Achilles may need to take a infinite number of steps to catch the tortoise but each step takes half the time to make as the previous step, so Achilles catches up in a finite amount of time. John K Clark -- You received this message because you are subscribed to the Google Groups "Everything List" group. To unsubscribe from this group and stop receiving emails from it, send an email to everything-list+unsubscr...@googlegroups.com. To post to this group, send email to everything-list@googlegroups.com. Visit this group at https://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/d/optout.
