# Why probabilities are measured over intervals (instead of points) for continuous probability distributions? [duplicate]

In case of discrete probability distributions, we find probabilities of different points/values over exactly those points, but in case of continuous probability distributions, we find probabilities of points within intervals --- why is that ? Can we not find out probability of a continuous random variable at a given point without the interval?

• We can -- but it is always zero. Oct 3 '19 at 17:02
• @Nick So it approaches zero as the number of possible outcomes approaches infinity? It is not actually zero but is approaching zero ? Oct 3 '19 at 17:32
• Probability zero is a subtle concept. The entire probability is always 1. How that can be reconciled with what I said requires some careful explanations. I was sparse with a comment because I was trustful that someone would identify a duplicate. Oct 3 '19 at 17:40
• depending on the power of a set a sum of zeros can be zero or more than zero Oct 3 '19 at 19:26