About predicting an event in future.

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The discussion centers on the nature of predicting future events and the concept of probability. It argues that while anything can happen in the future, once an event occurs, it becomes a singular past event, leading to a probability of 1/∞, which is effectively zero. This reasoning holds in continuous probability spaces, where the likelihood of any specific event happening is also zero due to the infinite nature of decimals. In contrast, discrete probability spaces may not follow the same logic. Time series analysis is suggested as a method to predict future events based on past patterns, which alters the probabilities involved.
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we know anything can happen in future.but when future becomes past only one event has actually occurred. so the probability of any future event is 1/∞ that is zero. so technically the event that has happened cannot occur.how do i understand this.
 
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The probability space of the event might not be infinite (ie discrete), then the argument above fails. In the continuous (infinite) case, we consider the probability over a region since the probability of any single exact event is zero. Think of it this way, the probability of two events happening exactly the same time is zero since you are always count down further decimals like .9923534525252626 to get more accuracy and eventually the numbers will differ in a large enough decimal place. I am not sure if this answers your question.

You can think in terms of time series, which assumes that the pattern in the past will continue in the future, then the probabilities of the future changes.
 
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The standard _A " operator" maps a Null Hypothesis Ho into a decision set { Do not reject:=1 and reject :=0}. In this sense ( HA)_A , makes no sense. Since H0, HA aren't exhaustive, can we find an alternative operator, _A' , so that ( H_A)_A' makes sense? Isn't Pearson Neyman related to this? Hope I'm making sense. Edit: I was motivated by a superficial similarity of the idea with double transposition of matrices M, with ## (M^{T})^{T}=M##, and just wanted to see if it made sense to talk...

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