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- Newsgroups: sci.math
- Path: sparky!uunet!brunix!brunix!dzk
- From: dzk@cs.brown.edu (Danny Keren)
- Subject: Re: Do you know ?
- Message-ID: <1992Oct16.151109.2325@cs.brown.edu>
- Sender: news@cs.brown.edu
- Organization: Brown University Department of Computer Science
- References: <1992Oct16.050019.25103@noose.ecn.purdue.edu>
- Date: Fri, 16 Oct 1992 15:11:09 GMT
- Lines: 24
-
- kavuri@lips.ecn.purdue.edu (Surya N Kavuri ) writes:
- #
- # Can you give me a function on an interval [a b] which is
- # not differentiable anywhere on that interval ?
-
- To make the question interesting, you have to ask for the function
- to be continuous (it is easy to construct functions which are
- nowhere continuous and hence nowhere differentiable).
-
- The famous example (by Weirstras I think) is
-
- sin(x)+sin(2x)/2+sin(4x)/4+sin(8x)/8+sin(16x)/16+...
-
- It is certainly continuous (by the M-test for instance) but
- nowhere differentiable.
-
- As a matter of fact, *most* continuous functions (most in a
- topological sense) are nowhere differentiable! See any good
- tpology text (Willard for instance) for more; look for the
- notion of category.
-
- -Danny Keren.
-
-
-