ABSTRACT
The metric space captures the “essential” qualities of measuring distance. There are four such properties: positivity; positive definiteness; symmetry; and triangle inequality. An important thing to note is that the same sets can have different metric functions assigned to them. This chapter discusses Euclidean metric and taxicab metric. One of the best consequences of introducing the concept of a Metric Space is that one can examine more abstract sets through this lens, bringing the concepts of analysis to more complicated, interesting spaces. Various metric spaces can be defined on subsets of this set when imbued with an appropriate metric. As sequence convergence and divergence are at the heart of Real Analysis, one is interested in understanding how to generalize these topics to the world of metric spaces. The intuitive idea of sequence convergence – that of a sequence getting “close” to a limiting value – can be nicely adapted using metrics and distance measurements.
