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Path: utzoo!lsuc!msb
From: msb@lsuc.UUCP (Mark Brader)
Newsgroups: net.puzzle
Subject: Re: Derivative of x! and actual interviews
Message-ID: <561@lsuc.UUCP>
Date: Mon, 1-Apr-85 19:36:28 EST
Article-I.D.: lsuc.561
Posted: Mon Apr  1 19:36:28 1985
Date-Received: Mon, 1-Apr-85 19:58:01 EST
References: <1337@decwrl.UUCP> <383@cavell.UUCP> <441@hou2g.UUCP>
Reply-To: msb@lsuc.UUCP (Mark Brader)
Organization: Law Society of Upper Canada, Toronto
Lines: 26
Summary: Be sensible

Bopsi Chandramouli writes:	

> > The necessary and sufficient condition for the derivative of a function
> > to be defined is that the function should be continuous (and x! is not).
> > Answering this question on the fly requires JUST clear thinking and good
> > understanding of the fundamentals of what one has learnt before. ...

J. Stekas responds:

> That question would weed out un-clear thinkers of the order of Ludwig
> Boltzman who built statistical mechanics on the large integer limit of
> the binomial distribution, [N!/(N-n)!n!]....
> 
> Perhaps the interviewer who used this question will one day be fortunate
> enough to face an equally petty interviewer.

I suggest that the proper response to this question in real life is:

"x! isn't differentiable, because it isn't continuous.  Or did you mean
the derivative of the gamma function, the real-number analog of x!?" (?!)

If the question is being posed in written form, I would stand with the
correct answer, i.e., the first one.  Anyone asking that question to
test my math who expects the derivative of gamma, I don't want to work for.

Mark Brader