Re: Mathematics to reconsider
Posted: Tue Jun 08, 2010 6:00 am
the problem with this question as normal is that not too many people took a real analysis course. which is all about proving theorems. i mean we could incorporate both heine-borel theorem and into the limits and continuity theorems. for a funciton defined on a neighborhood of a point, continuity at the point means the same thing as having a limit equal to the functional vale:
Theorem of 1.0=0.999. let f:s→R, where s is the neighborhood of c ɛ Ɽ.
a) Æ is continuous at c;
b) ÆŽ lim (sub) x→c(/sub) Æ(x) = Æ(c)
also here's some sources (had to find my old books and notes) The equivalence (a)↔(c) is due to S. Bnanach [cf. Hewitt and Stromberg, op. cit., p. 288 (18.25)], or see the author's article in paul halmos: celebrating 50 years of mathematics [springer-verlag, new york, 1991], p. 284 propositions.
imo ice cream still tastes good no matter what any people say.
Theorem of 1.0=0.999. let f:s→R, where s is the neighborhood of c ɛ Ɽ.
a) Æ is continuous at c;
b) ÆŽ lim (sub) x→c(/sub) Æ(x) = Æ(c)
also here's some sources (had to find my old books and notes) The equivalence (a)↔(c) is due to S. Bnanach [cf. Hewitt and Stromberg, op. cit., p. 288 (18.25)], or see the author's article in paul halmos: celebrating 50 years of mathematics [springer-verlag, new york, 1991], p. 284 propositions.
imo ice cream still tastes good no matter what any people say.
