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And it’s not “overwhelmingly likely” as in there’s a 99% chance or whatever. If you choose a random point on the line, the probability of choosing a rational is
by wat10000 2y ago
And it’s not “overwhelmingly likely” as in there’s a 99% chance or whatever. If you choose a random point on the line, the probability of choosing a rational is zero.
- IanKerr 2y agoYep, exactly. I glossed over that detail a bit because explaining how a meagre set has a truly zero probability of being picked, while technically still being a possible result of a random process, is a bit messy to wrap your head around colloquially.
- alexashka 2y ago> If you choose a random point on the line, the probability of choosing a rational is zero. Wat? If a thing is in my pocket, there's an above zero probability of me picking it when I randomly take a thing out of my pocket. What are math people doing that's different?
- josephcsible 2y ago> Do math people not feel the need to explain themselves when they state things that defy common sense everyone except math people agree upon? Is that part of thinking you're 'smart'? It's a pretty basic thing covered in undergrad prob/stats classes. We don't re-explain it every time we use it for the same reason computer scientists don't re-explain the halting problem every time it comes up.
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- BalinKing 2y ago> If a thing is in my pocket, there's an above zero probability of me picking it when I randomly take a thing out of my pocket. This is only true if there are only a finite number of things in your pocket, though… I think an analogy is how we always have 1/n>0 for any finite (positive) number n—and yet, 1/infinity=0. For something more precise, I think the corresponding Wikipedia page (FWIW) is https://en.wikipedia.org/wiki/Almost_never https://en.wikipedia.org/wiki/Almost_never.
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- wat10000 2y agoThey’re working with infinity. Your pocket is not infinite. Numbers are.
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