Indicate whether the following statements are true or false

1.A sequence {an} can have more than one limit.

2.A sequence {an} that has no limit diverges

3.the sequence {1,-1,1,-1..}has two limits.

4.If lim n->inf {an}=L and Lim n-> inf{bn}=M then lim n->inf {an bn } =LM

5 f(x)=(x^2-1)/(x-1) and g(x) =x+1 are same function