Later: She went to the party and not a single f*** was given that day.
No. The universe exploded. It's 2012, man!
Does Pr(X) = 0 mean that it is impossible to happen?
If I pick a rational number between 0 and 1, the chances of picking exactly 0.5 are 0 [Pr(x=0.5)=0], but it doesn't mean it is impossible.
Actually, I believe it is impossible. 0.5 is also .50000...0...
The probability that any given digit is 0 would be 1/10. Further,
lim (as t->infinity) of (1/10)^n=0. Therefore, it can't happen.
Damn he got there first, and is right. Impossible implies probability is zero, but it doesn't go back the other way. http://en.wikipedia.org/wiki/Almost_never sort of covers it.
"if" =/= "iff"
Your point would work if you instead picked a random real between 0 and 1, as there is no uniform distribution on a countably infinite set. (If the probability of each number is 0, then 1 = Pr(anything) = SUM_q(Pr(x=q)) = SUM_q(0) = 0, by countable additivity). Picking a random real works fine, however, as probabilities are not required to satisfy uncountable additivity.
But the other way around is true. If it is never going to happen, then Pr(x)=0.
There is the possibility that he was rounding off a fairly small, statistically insignificant probability. And thus the universe was saved!
Also, circles do not exist (rounding pi to the 10's place, pi=0). Teach the controversy!
A new nice comic came up!!! (party)
Mike, looks like the fund grows rapidly, doesn't it? :-D
Cheers and nice math to all!!!
Indeed it does! Looks like I techinically missed 8 updates and I've covered for six so far, so still owe for two.
Not if she asks continuously an infinite number of times during a finite interval of time.
Since there is a possibility, however small, that she will end up at the party, Pr(x) > 0. Even if it is not > 10^-100.
So the Universe is saved!
Isn't the universe still in the process of exploding? That would make this one of those cases where it doesn't matter what the input to the if then statement is.
No, it's expanding, not exploding.
But the expansion is the tail end of an explosion.
He is lucky that she is not a Bayesian. If she had been a Bayesian, she just would have interpreted his words as an evidence, evaluated Pr(X|My father says that Pr(X)=0), concluded that it is non-zero and went to the party anyway.
Checking spiked math is the first thing I do in the morning!!! :-)
Keep up the good work! :-)
Probability zero does not mean it cannot happen. Suppose I randomly pick an integer what is the probability I pick 63? It's zero, but I still could pick 63.