On Mon, Oct 29, 2018 at 2:36 PM Philip Thrift <[email protected]> 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 [email protected]. To post to this group, send email to [email protected]. Visit this group at https://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/d/optout.
