Problem 1: Given the metric space (X, p), prove that
a) |p(x, z) - p(y, u)| < p(x, y) + p(z, u) (x, y, z, u is an element of X);
b) |p(x, y) - p(y, z)| < p(x, y) (x, y, z is an element of X).
These problems are from Metric Space. Please give formal proofs for both (a) and (b) based on the reference provided. Thank you.
This solution provides a step by step response which illustrates how to approach solving metric space proofs. The solution is provided in an attached Word document. Two Word documents, with the exact same solution, have been provided, one in the 2003 format and the other in the 2007.