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 Mar 20 comment Mean number of unique choices given n people choosing randomly from a set of N elements Right, I think that bypasses the problem that was nagging at me. Thanks. Mar 20 comment Mean number of unique choices given n people choosing randomly from a set of N elements I can't quite put my finger on it... but since the outcomes are not independent of one another, is $E(X)$ really equal to $\sum_i E(X_i)$? Mar 19 comment Mean number of unique choices given n people choosing randomly from a set of N elements I was just wondering if failing to incorporate this constraint in the model gives the wrong probabilities. I vaguely remember that indicator variables miraculously get around some such problems, but I'm not sure here so I thought I'd ask. Mar 19 comment Mean number of unique choices given n people choosing randomly from a set of N elements Since everyone has to choose some destination, the probability that all $X_i = 0$ simultaneously is zero. Your model seems to assign non-zero probability to this... or does it? Mar 19 comment If I ask $1000$ people to choose a random number between $0$ and $999$, what is the probability that no one will choose a specific number? David, Not according to the way $x$ is chosen, and not according to the OP's code (see link). But the question doesn't match the code, so one of the two is wrong. Since I doubt the OP really intends $x$ to be drawn from a larger range of numbers than people can choose from, I'll assume the code is correct until the OP clears this up. Mar 19 comment If I ask $1000$ people to choose a random number between $0$ and $999$, what is the probability that no one will choose a specific number? Wait, people really choose numbers in the range $[0, 999]$, but your $x$ is in the range $[0, 1000]$? Your code uses $[0, 1000]$ for both. Mar 19 revised If I ask $1000$ people to choose a random number between $0$ and $999$, what is the probability that no one will choose a specific number? added 42 characters in body Mar 19 revised If I ask $1000$ people to choose a random number between $0$ and $999$, what is the probability that no one will choose a specific number? added 96 characters in body Mar 19 answered If I ask $1000$ people to choose a random number between $0$ and $999$, what is the probability that no one will choose a specific number? Mar 15 comment Is there any uncountably infinite set that does not generate the reals? @NoahSchweber that makes sense, thanks! Mar 15 comment Is there any uncountably infinite set that does not generate the reals? @Ricky, I don't see why: By construction, the maximal element of ℙ does not even generate the reals-- let alone be equinumerous to them. Mar 15 comment Is there any uncountably infinite set that does not generate the reals? "By Zorn's lemma ℙ has a maximal element, and it's not hard to show that such an element can't be countable." Could you sketch an argument for this? It seems to boil down to the original question... Feb 26 awarded Yearling Nov 20 comment Probability of picking a certain option at least once in two tries Your calculation gives the probability that he teleported to work and teleported back. That's what multiplying the probability of two events does. Nov 14 comment If A is infinite, does there have to exist a subset of A that is equivalent to A? Thanks for the clarifications, everyone. My curiosity is satisfied by the role of the AoC in the "obvious" construction. So Rudin's "is not finite" means "there is no bijection to an element of $\mathbb N$? Nov 12 comment If A is infinite, does there have to exist a subset of A that is equivalent to A? Is the axiom of choice really needed for the first step? Why? Oct 23 comment Non-Euclidean Geometry for Children Sounds like you can just give Flatland to your son, and he will make the effort of bringing it to bear. Sep 10 comment What is exactly the difference between a definition and an axiom? @Bye, the defining properties of a vector space don't need to hold axiomatically: For example, $\mathbb R \times \mathbb R$ is a vector space because of the predefined properties of addition and multiplication. You can also study vector spaces in the abstract (i.e. vector spaces have all the defining properties because they are vector spaces), but that's a different thing. Sep 9 revised Finding x in an Olympiad simultaneous equation deleted 7 characters in body Sep 8 revised Finding x in an Olympiad simultaneous equation added 185 characters in body