Assignment:
Q1. Let P be the set of all functions f : N -----> N such that for some M in N and all n>M, f(n + 1) = f (n). In other words, f is in P provided that after some point, f is constant. Show that P is countable.
Q2. Let E be the set of all strictly increasing functions f : N ----> N. Show that E is uncountable.
Provide complete and step by step solution for the question and show calculations and use formulas.