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- From: hrubin@pop.stat.purdue.edu (Herman Rubin)
- Newsgroups: sci.math
- Subject: Re: Apology about f'(g(x))
- Message-ID: <BxMDuM.7qy@mentor.cc.purdue.edu>
- Date: 12 Nov 92 20:20:41 GMT
- References: <Bx5EJD.CtG@unix.amherst.edu> <3NOV199214312961@venus.tamu.edu> <BxLtv5.93H@newcastle.ac.uk>
- Sender: news@mentor.cc.purdue.edu (USENET News)
- Organization: Purdue University Statistics Department
- Lines: 29
-
- In article <BxLtv5.93H@newcastle.ac.uk> A.M.Wall@newcastle.ac.uk (A.M.Wall) writes:
- >So you are all arguing about the following:
-
- > df
- >Is f' a function, with value --, or does f'(y) mean "take f and differentiate
- > dx
- >wrt y"? The answer is probably that both are perfectly good interpretations,
- >but that the former is more widely accepted. If you need to use the latter,
- > df(g(x))
- >then the full notation -------- is less confusing (whether or not you actually
- > dg(x)
- >prefer it).
-
- There are larger logical problems with this latter notation than you
- realize. We are in a situation where precise notation is needed, and
- even saying that f'(x) = df/dx is WRONG. If f is a function with a
- domain which is a subset of the real numbers, then f' is a function
- with a domain a subset of the interior of the domain of f. But it
- is a function. And the function f is not f(x).
-
- Those who think this pedantic are hereby advised to read some books on
- the Calculus of Variations; it is necessary there that these distinctions
- are made.
-
- --
- Herman Rubin, Dept. of Statistics, Purdue Univ., West Lafayette IN47907-1399
- Phone: (317)494-6054
- hrubin@snap.stat.purdue.edu (Internet, bitnet)
- {purdue,pur-ee}!snap.stat!hrubin(UUCP)
-