An uncountable countable set
in [Math]
|
Prev: integral problem
Next: Prime numbers
From: MoeBlee on 25 Sep 2006 15:40 Han.deBruijn(a)DTO.TUDelft.NL wrote: > MoeBlee schreef: > > > Han de Bruijn wrote: > > > Absolute also means that e.g. an Alien Civilization can understand those > > > axiomatized theories. What makes you think that such will be the case? > > > > I can't predict what will be understood by aliens. But for certain > > systems, it is computable whether a string of symbols is or is not an > > axiom and it is computable whether a given string of symbols is or is > > not a proof. > > I'm still flabbergasted why those difficult proofs as for Fermat's Last > Theorem or the Poincare Conjecture are not proved then with the full > power of modern computers. That doesn't even make sense to me. Anyway, I'm not referring to using computers to search for proofs. MoeBlee
From: Han.deBruijn on 25 Sep 2006 15:45 Virgil wrote: > Def: 0.333... = lim_{n -> oo} Sum_{k = 1..n} 1/3^n Oh? 1/3 + 1/9 + 1/27 + 1/81 + 1/243 + 1/729 + ... > 4.993141289 > 0.333 Han de Bruijn
From: Han.deBruijn on 25 Sep 2006 15:53 Han.deBru...(a)DTO.TUDelft.NL schreef: > Virgil wrote: > > > Def: 0.333... = lim_{n -> oo} Sum_{k = 1..n} 1/3^n > > Oh? > > 1/3 + 1/9 + 1/27 + 1/81 + 1/243 + 1/729 + ... > 4.993141289 > 0.333 Even worse: lim_{n -> oo} Sum_{k = 1..n} 1/3^n = 1/2 = 0.5 . No? Han de Bruijn
From: MoeBlee on 25 Sep 2006 15:56 Han.deBru...(a)DTO.TUDelft.NL wrote: > Paul Halmos, "Naive Set Theory", Princeton 1960. I like that book, but it's only a summary, not a full textbook. > E. Nagel, J.R. Newman, "Goedels Proof", New York, 1968. That's a fairly non-technical discussion of just one aspect of mathematical logic. Neither of those books are what I have in mind. MoeBlee
From: Gerard Schildberger on 25 Sep 2006 16:01
| Han.deBruijn wrote: |> Virgil wrote: |> Def: 0.333... = lim_{n -> oo} Sum_{k = 1..n} 1/3^n | Oh? | | 1/3 + 1/9 + 1/27 + 1/81 + 1/243 + 1/729 + ... > 4.993141289 > 0.333 | | Han de Bruijn Oh? I get .49999999999999999999999999999999999+ when using a precision of 60 digits and 100 terms. ____________________________________Gerard S. |