Assignment:
Define a new metric d on X = (0, 1/2)2 by d((a,b), (r,s)) = 1 if a is not equal to r Or |b - s| if a = r.
a) Show that d is a metric on X.
b) What are the compact subsets of X? Prove your statement.
Provide complete and step by step solution for the question and show calculations and use formulas.