Does it bother you, Brad, that if S is a Cantor set in R, card (S) = card (R) but S is measure zero in R? On Thu, Aug 8, 2019, 4:18 AM <bradklee@gmail.com> wrote:
For reals R, card(R^n)=card(R) yet R is measure zero in R^n. This is something of a paradox, yet:
R^n=(R^(n-1)/p)*R + p*R,
with p a lone point of R^(n-1), and p measure zero in R^(n-1). This sounds okay(?).
What’s more troubling is reading on stack exchange and physics forum that Lebesgue integration allows, sometimes requires (?), 0*infinity=0?
“I’m on the outside, looking inside / what do I see? / Much confusion, disillusion / all around me.”
Arggggg.......
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun