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Math Forum » Discussions » Inactive » Historia-Matematica

Topic: [HM] Weierstrass, pathological functions
Replies: 2   Last Post: Aug 25, 2000 11:11 PM

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Everdell@aol.com

Posts: 155
Registered: 12/3/04
Re: [HM] Weierstrass, pathological functions
Posted: Aug 25, 2000 11:11 PM
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Sam Kutler asks:

<<But, Bill and all, is that function what we had meant by continuous[?]
Sure, we meant that we can change f(x) by as little as possible by changing
x by a small enough distance, but didn't we mean more than that?>>

I submit that what we (mathematicians and other thinkers) mean by
"continuous" is in the highest degree problematical, and as philosophical
as it is mathematical. At least since Dedekind. Certainly since Robinson.
The more I can learn about the question, the better.

Bill Everdell, Edgartown, MA

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