Ted Ersek
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 Aug 30 comment We all use mathematical induction to prove results, but is there a proof of mathematical induction itself? "then we can infer that (iii) all numbers have Property P." I think you mean "then we can infer that (iii) all Natural numbers have Property P." May 25 awarded Notable Question Feb 22 awarded Commentator Feb 22 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? Sep 24 awarded Autobiographer Jul 2 awarded Curious Feb 10 awarded Yearling Jan 6 accepted Generality of Lebesgue integration? Jan 6 accepted Do we have a notation for a quantity that is smaller or larger than x by an infinitesimal amount? Jan 6 asked Generality of Lebesgue integration? Jan 6 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. Jan 6 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. Jan 5 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 .... Jan 5 asked Do we have a notation for a quantity that is smaller or larger than x by an infinitesimal amount? Jan 5 accepted $\infty\pm\infty$ on a Riemann sphere Jan 4 awarded Supporter Jan 3 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. Jan 3 revised $\infty\pm\infty$ on a Riemann sphere added 377 characters in body Jan 2 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. Jan 1 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.