A function f satisfying f(0)=card(R) isn’t the sort of function treated in any flavor of real analysis I’ve seen, because card(R) is a cardinal, not a real number. I expect that it would be hard to create an extension of real analysis that would treat such things in a consistent and interesting way. The closest thing to what Brad is imagining (that I’m aware of) is surreal analysis, which is fraught with difficulty. Jim Propp On Tue, Aug 13, 2019 at 12:52 PM Brad Klee <bradklee@gmail.com> wrote:
Lebesgue Commandment: Ignore all measure zero sets. Numerical Recipe: Only calculate measure zero sets.
In the other thread, we are talking about computational practice, so I'm spinning this response another direction. See also the other thread "Loosing sleep because..." :
https://mailman.xmission.com/cgi-bin/mailman/private/math-fun/2019-August/03...
Instead of "0*Infinity = 0", perhaps it should be card(Z)*(1/card(R))=0. Then what if the function is allowed to take on a value f(0)=card(R)? Is it still okay to ignore the one-point set at t=0?
You're welcome to keep up the antagonism, but please try not to make me look like too much of an idiot.
Thanks --Brad
On Fri, Aug 9, 2019 at 8:24 PM Andy Latto <andy.latto@pobox.com> wrote:
The definition of Lebesgue integration is a fairly fundamental part of analysis. What about it worries you? Andy
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