Recently, I learned that, in a probability density function, the probability of the occurrence of any specific x-value is in fact zero, for the relevant interval on the function is a point, which has zero width and therefore has zero area associated with it under the probability curve. This made me realize that, although I understand how Riemann sums work for intervals of >0 width, I cannot make sense of the concept of an integral once the constituent intervals become point-sized (i.e., an interval of 0 width multiplied by any finite y-value will always produce a partition of 0 area). More generally, this means I don't understand how a collection of adjacent points can form a line having nonzero dimensions. Presumably there is a relatively simple explanation of how to conceptualize this, but I can't find anything. Any guidance would be appreciated. Thank you.