- If p is a prime number, show that is irrational.
- Show that
- Show that if , then the number is an irrational number.
- Show that if and are two Cauchy sequences, then so are and .
- If A and B are non empty subsets of that is bounded below. Then, if and only if (i) for all and (ii) for any , .
Reference: A Second Course in Analysis by M Ram Murty, Hindustan Book Agency.