Ted Ersek
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 Feb22 awarded Commentator Feb22 comment $\infty\pm\infty$ on a Riemann sphere @ChristianBlatter, I was thinking about this again. In Mathematical Analysis, 2nd Ed., section 1.33 Thomas M. Apostol says Inf+Inf=Inf when Inf is the Point at infinity on the extended complex plane. Can Apostol get away with this because he is not working in the framework of field axioms, or do you maintain that Apostol is wrong on this point? Sep24 awarded Autobiographer Jul2 awarded Curious Feb10 awarded Yearling Jan6 accepted Generality of Lebesgue integration? Jan6 accepted Do we have a notation for a quantity that is smaller or larger than x by an infinitesimal amount? Jan6 asked Generality of Lebesgue integration? Jan6 comment Do we have a notation for a quantity that is smaller or larger than x by an infinitesimal amount? @Stephen Montgomery-Smith, Make it an answer, and I will accept it. Jan6 comment Do we have a notation for a quantity that is smaller or larger than x by an infinitesimal amount? @Han de Bruijn, Error is a totally different topic. Using the notation mentioned above by Stephen Montgomery-Smith "2+" is a quantity that is larger than 2 by an infinitely small amount. Also "2-" is smaller than 2 by an infinitely small amount. A useful application is ArcTan(0-) = -Pi/2. Jan5 comment Do we have a notation for a quantity that is smaller or larger than x by an infinitesimal amount? @E.O. What's wrong with limits? Complicated things will be more readable if we have concise notation. We may have never found solutions to PDEs if the were expressed in terms of: For every epsilonX, epsilonY, there exists a deltaX, deltaY such that .... Jan5 asked Do we have a notation for a quantity that is smaller or larger than x by an infinitesimal amount? Jan5 accepted $\infty\pm\infty$ on a Riemann sphere Jan4 awarded Supporter Jan3 comment $\infty\pm\infty$ on a Riemann sphere @Christian Blatter, It makes sense to me to say
$z\cdot\infty = \infty$ for any complex non-zero $z$.
and the book Mathematical Analysis by Tom Apostol says this as well. Your second sentence agrees with this, but your first sentence says it is one of the things that are undefined. Please clarify. Jan3 revised $\infty\pm\infty$ on a Riemann sphere added 377 characters in body Jan2 comment $\infty\pm\infty$ on a Riemann sphere I like the explanation of "undefined" vs "indeterminate". That point has puzzled me for a few years. I am an electrical engineer with a strong interest in math. Jan1 comment $\infty\pm\infty$ on a Riemann sphere @Michael Hardy, I like the precise definition of Indeterminate. All other explanations I have read are hand wavy. Jan1 comment $\infty\pm\infty$ on a Riemann sphere I recall reading it in a text book I left at work. I will check the book when I get to work tomorrow. Although I see en.wikipedia.org/wiki/Riemann_sphere says Inf +- Inf are both undefined. Jan1 asked $\infty\pm\infty$ on a Riemann sphere