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## Main Question or Discussion Point

What really is a probability density function for continuous random variables? I know that the probability for a single value occurring in a continuous probability distribution is so infinitesimal that it is considered 0, which is why we use the cumulative distribution function that is the the integral of the PDF from -∞ to some number x. However, if any single value in the PDF is 0, then how to we get a density curve and how are we able to integrate the PDF if all of its values (probabilities) are zero?