uniqueness of limit of sequence
If a number sequence has a limit, then the limit is uniquely determined.
Proof. For an indirect proof (http://planetmath.org/ReductioAdAbsurdum), suppose that a sequence
has two distinct limits and . Thus we must have both
But when exceeds the greater of and , we can write
This inequality an impossibility, whence the antithesis made in the begin is wrong and the assertion is .
|Title||uniqueness of limit of sequence|
|Date of creation||2013-03-22 19:00:23|
|Last modified on||2013-03-22 19:00:23|
|Last modified by||pahio (2872)|