Hi, I have been told that the following two statements are true, but I don't have a clue how to actually prove it. I have been told that I can either prove it with words or with an example... :S

1.- If the sequence ($\displaystyle a_n$) has a limit and the sequence ($\displaystyle b_n$) is such that $\displaystyle a_j=b_j$ whenever $\displaystyle j>10^{100}$ then the sequence ($\displaystyle b_j$) has a limit.

2.- Every real number r is the limit of a sequence all of whose terms are rational numbers.