A density is a continuous
non-negative function defined on all the reals
and such its integral is equal to 1.
For B=[a,b] an interval:
If we take b=a, we see that for all a, the probability that a continuous random variable takes on that value is 0, this is the big difference with discrete random variables.
Intuitively for a very small width
will be proportional to
the density at x: