Dangerous limits ... Tommy's limit paradox - Printable Version +- Tetration Forum (https://math.eretrandre.org/tetrationforum) +-- Forum: Tetration and Related Topics (https://math.eretrandre.org/tetrationforum/forumdisplay.php?fid=1) +--- Forum: Mathematical and General Discussion (https://math.eretrandre.org/tetrationforum/forumdisplay.php?fid=3) +--- Thread: Dangerous limits ... Tommy's limit paradox (/showthread.php?tid=1039) Dangerous limits ... Tommy's limit paradox - tommy1729 - 11/27/2015 Not so much related to tetration but I just wanted to warn about limits. Limits , induction and infinity are imho poorly used and understood. For a simple example 1/1 + 1/4 +1/9 + 1/16 + ... The truncated sum after n additions is Always rational. No matter how Large n is. However the (complete) Sum = zeta(2) = irrational. But that is Well known. Tommy's limit paradox Quiz F(1) = 1/3 F(2) = 1/3 + 1/9 + 1/27 ... Is (-2) ^( F(oo) ) = A) sqrt(-2) = sqrt(2) i Most students say " Yes ofcourse ! " B) the solution set {sqrt(2) i , - sqrt (2) i ) C) (-2)^0,499999... D) - 2^(1/4 + 1/8 + ...) E) - sqrt(2) F) cant say G) other. Regards Tommy1729