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Re: A riddle: Functions that return unevaluated when they cannot

• To: mathgroup at smc.vnet.net
• Subject: [mg82502] Re: A riddle: Functions that return unevaluated when they cannot
• From: P_ter <peter_van_summeren at yahoo.co.uk>
• Date: Mon, 22 Oct 2007 05:43:48 -0400 (EDT)

In The Mathematical Journal Volume 7, issue 2 there is an article from Bruce Miller "A function which does not evaluate".(page 149).
Sin[x] does not evaluate because x is undefined.
f[q_?NumberQ]:= q^2 gives with f[x]: f[x] and with f[2.718] 7.38752.
Of course, again and again: Clear[f]
But, with
f[(n_?Positive)?IntegerQ]:=n!
f[n_]:= Print["f expects a positive integer argument"]
Try f[2.4]
It is the way some functions are implemented that they do not a "should" evaluate.
with friendly greetings,
P_ter