Hello! I need some help with these problems...

1. a. Prove that the set of all strictly increasing sequences of natural numbers, is not a countable set.

b. What can you say about the set of converging sequences of natural numbers? Is it a countable set, or not?

c. The same question about the set of periodic sequences of natural numbers.

2. Find out a function f:R->R, f injective, f not surjective.

Thank you!