"Irrational" limit behavior

*To*: mathgroup at smc.vnet.net*Subject*: [mg44390] "Irrational" limit behavior*From*: "David W. Cantrell" <DWCantrell at sigmaxi.org>*Date*: Fri, 7 Nov 2003 05:16:57 -0500 (EST)*Sender*: owner-wri-mathgroup at wolfram.com

Near the end of August, Maxim noted a limit which is clearly not 0, yet which Mathematica claims to be 0 . It had the form Limit[x - Sqrt[Pi], x -> q] where q was merely a very close rational approximation of Sqrt[Pi]. Here's a similar example: In[1]:= Rationalize[Sqrt[E], 10^(-74)] Out[1]= 34967586868203284666575423396341074438/21208913531730155539833556128356679037 In[2]:= Limit[x - Sqrt[E], x -> %] Out[2]= 0 I find this "irrational" behavior to be extremely disturbing. Please, someone, explain to me what's going on! David Cantrell