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"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