Limit vs limit point. #limit #point #metric #space #convergent #cauchy
In the previous section we see the convergent and Cauchy sequences in a metric space with their properties. We see that a limit point is a point to which a sequence is convergent. Also every convergent sequence in a metric space is a Cauchy sequence and the converse of the theorem i.e., every Cauchy sequence is not convergent.We illustrate it with an example by considering (0,1] as metric space and a sequence {1/n} which is Cauchy but not convergent in (0,1] in detail. In the following there is an introduction to few points and few definitions. Now take a look upon them. Contents : 1. Limit vs limit point 2. Every where dense or dense set 3. Nowhere dense set 4. Boundary and boundary point of a set 1 . Limit vs limit point :- Some times we often use the terms limit and limit points. Are they both have same meaning? This is a confusion to every reader. On the real line...
