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Integer Element assumptions not always consistent?

• To: mathgroup at smc.vnet.net
• Subject: [mg20174] Integer Element assumptions not always consistent?
• From: Jim Radford <radford at robotics.caltech.edu>
• Date: Sun, 3 Oct 1999 21:07:40 -0400
• Organization: California Institute of Technology, Pasadena
• Sender: owner-wri-mathgroup at wolfram.com

I'm very pleased that Mathematica 4.0 has support for assumptions in
Simplify, but my first attempt to use them produced inconsistent
results.  I traced the problem to the following

Limit[    Sin[2 n Pi]/(n-1), n->1]                 (* 2 Pi *)
Simplify[ Sin[2 n Pi]/(n-1), Element[n,Integers]]  (*  0   *)

I'm not sure what form I would expect back from the Simplify,
but maybe some thing like:

  n==1 && 2Pi || 0

which isn't really the correct form because it is not Boolean, but I'd
like it to return something analogous to what Reduce returns.  If
nothing else I would expect an "Indeterminate" message of some kind.

Is this a bug or a feature?

-Jim