Reputation
507
Top tag
Next privilege 1,000 Rep.
Create new tags
Badges
4 10
Impact
~5k people reached

  • 0 posts edited
  • 0 helpful flags
  • 5 votes cast
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<br> $z\cdot\infty = \infty$ for any complex non-zero $z$.<br> 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.
Jan
1
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.