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It isn't, actually. There is a difference between discrete and continuous probability distributions. Lotto numbers are a classic example of a discrete, finite s
by jknoepfler 10y ago
It isn't, actually. There is a difference between discrete and continuous probability distributions. Lotto numbers are a classic example of a discrete, finite space, and the probability of winning the lottery can be expressed precisely as a non-zero number. The probability of any individual event in a continuous probability distribution is exactly zero. You're free to dispute whether the continuum as a mathematical construct has validity when applied to the world of actual stuff, but that's a different debate and certainly doesn't have an obvious answer.
- noobermin 10y agoThat's why you don't quote probabilities from continuous PD's as "the probability of X" but of X falling between a range. It's like you're saying the area under a point on the graph is zero...duh.
- mrob 10y agoIt's not a different debate, it's an essential requirement for zero probability events to actually happen. For zero probability events to happen the observable universe needs to contain infinite bits of information. The true upper bound is subject to debate but it's widely believed to be finite (eg. below the Bekenstein bound). If it is finite, then by the pigeonhole principle, no method of sampling a continuous distribution can choose between more points from that distribution than can be enumerated by that many bits. This means the probability of making any specific selection is non-zero, because almost all of the distribution cannot be selected.