> On 29 Oct 2018, at 17:54, agrayson2...@gmail.com wrote: > > > > On Monday, October 29, 2018 at 4:07:41 PM UTC, John Clark wrote: > On Sun, Oct 28, 2018 at 2:56 PM <agrays...@gmail.com <javascript:>> 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. 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 everything-list+unsubscr...@googlegroups.com > <mailto:everything-list+unsubscr...@googlegroups.com>. > To post to this group, send email to everything-list@googlegroups.com > <mailto:everything-list@googlegroups.com>. > Visit this group at https://groups.google.com/group/everything-list > <https://groups.google.com/group/everything-list>. > For more options, visit https://groups.google.com/d/optout > <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 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.
