Introduction to Point-Set Topology
... nonnegative integer; hence a nonnegative real number. Certainly
d(x, y ) = d(y , x). If x = y (that is, x and y are the same word),
then x and y will not differ in any entry, in which case d(x, y ) = 0.
However, if x 6= y , then x and y will differ in at least one entry, so
d(x, y ) > 0.
We have the ...