On Tuesday, October 30, 2018 at 9:45:09 AM UTC, Bruno Marchal wrote: > > > On 29 Oct 2018, at 17:54, [email protected] <javascript:> wrote: > > > > On Monday, October 29, 2018 at 4:07:41 PM UTC, John Clark wrote: >> >> On Sun, Oct 28, 2018 at 2:56 PM <[email protected]> wrote: >> >> > *What's your view of Zeno's paradox which implies motion is >>> impossible.* >> >> >> 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. >> >> John K Clark >> > > This doesn't resolve Zeno's paradox. AG > > > > It does. >
*I don't think you understand Zeno's paradox. Why don't you state it in your own words to test your knowledge?. AG* The greeks understood that an infinite sum can converge. The math was not > rigoroius, and they wrongly believed that it is enough that the general > term tend to zero for the series to converge, which will be refuted many > centuries later by Oresme (a French bishop and mathematician) with the > harmonic series: > 1 + 1/2 + 1/3 + 1/4 + 1/5 + …. which diverges (like ln(n)). > Cauchy made the math rigorous here, and mathematical logic even > rehabilitates the infinitesimals of Newton and Leibniz, but, Imo, Cauchy > works is better. > > Bruno > > > > > > > > -- > 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] <javascript:>. > To post to this group, send email to [email protected] > <javascript:>. > Visit this group at https://groups.google.com/group/everything-list. > For more options, visit https://groups.google.com/d/optout. > > > -- 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.
