unique limit: circular argument. undefined symbols in main argument.
2 BIG mistakes.
several of my students referred to your page
http://mathonline.wikidot.com/uniqueness-of-a-convergent-sequence-s-limit
they lost most of their credit.
In eqn (2) the n in a_n is undefined, meaningless. The earlier \forall has long expired.
The proof of the lemma (top) is circular. Absolute nonproof. 0/10 points.
Easiest: Prove the contrapositive and invoke the Archimedean axiom/theorem
(if working with the reals defined axiomatically).
*
Matthias Kawski, President's Professor http://math.asu.edu/~kawski
School of Mathematical & Statistical Sciences ude.usa|ikswak#ude.usa|ikswak
Arizona State University office: (480) 965 3376
Tempe, Arizona 85287-1804 cell: (480) 406 3801
*