For each of the statements I need to show why they are not the correct definition. So either provide an example that satisfies the sequence and doesn't converge, or converges and satisfies the sequence. I just need an idea of how to do it, so any help would be great.
- for every epsilon>or=0 there exists N element of natural numbers such that for every n>or=N |xn -l|< epsilon
- for every epsilon>0 there exists n a natural number such that |xn -l|< epsilon
- there exists N element of natural numbers that for every epsilon>0 for every n>or=N such that |xn -l|< epsilon