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 Aug31 comment Surprise exam paradox? I don't quite understand why the knowledge gets represented as a partition of the states of the world. Isn't it possible that in one situation we know the world is in state A or B and in another we know it is in A or C? Jun1 comment A challenge by R. P. Feynman: give counter-intuitive theorems that can be translated into everyday language If the question is written as, "We search until we find a parent who has two children with one a boy born on a Tuesday and the other is not a boy born on a Tuesday", then it's much more obvious what is going on Mar15 comment Function to create a smooth, monotonically non-decreasing curve between three points @DavidH: That's a nice solution for the simple problem. Now if only there was a way to get the gradient to 0 at the end (in some cases the gradient might be heading towards minus infinity instead of 0) Mar15 comment Function to create a smooth, monotonically non-decreasing curve between three points @Bitrex: Sure. It would be nice if it weren't just smooth in terms of gradient - but had continuous higher order derivatives too, but I won't say that that is strictly necessary Nov1 comment Why is the collection of all groups considered a proper class rather than a set? Thanks, I can see how that'd apply to the other types as a well. If anyone else is reading this: Cantor's paradox proves that the collection of cardinals isn't a set Jul25 comment Do your friends on average have more friends than you do? To clarify my previous comment: deg u and deg v are the degrees of the vertices after the graph has been completed. As it is worded, my comment could have been incorrectly interpreted to be referring to a situation where a graph is built one edge at a time and the degree is the degree at this stage of construction. That is probably why I didn't spot this solution - you consider the effect that each edge being added separately has at the end, rather than the effect right now. Apr10 comment Nash equilibria - Why can we calculate a player's strategy without reference to their payoffs? Thanks for clarifying the Nash equilibrium issue. The issue I don't understand is it is possible to calculate a players optimal strategy without considering their payoffs. We found q=1/2, but we only used player 1's payoffs! Nov25 comment What are the Axiom of Choice and Axiom of Determinacy? Did you mean f(p(x))=x for equivalent 3? Apr16 comment Why are differentiable complex functions infinitely differentiable? Correct, but the derivative of a constant is 0, so the linearity is trivial. It only becomes interesting when we consider the derivative as a transformation from functions to functions Apr15 comment Why are differentiable complex functions infinitely differentiable? Interesting, although the derivative is not a linear transformation from R2->R2, but from f(R2)->f(R2) Dec15 comment Do your friends on average have more friends than you do? That's a very nice proof. So the core observation is that each edge contributes 2 to the total number of friends, but deg u/deg v+deg v/deg u to the number obtained by adding each person's friend popularity. Also, its worthwhile noting that 2≤x/y+y/x is easily proved using either calculus or the AM-GM inequality, just in case anyone doesn't know that Dec15 comment Do your friends on average have more friends than you do? @J.M. I have provided an exact graph theory question that should be answerable mathematically. Does sum(t/f)>sum(f) hold for all graphs or is there a counter example? Oct6 comment What mathematical questions or areas have philosophical implications outside of mathematics? @Peter: Book recommendations are welcome, though I don't know how long it will take me to look at them Oct5 comment What are the most important questions or areas of study in the philosophy of mathematics? @Robin: Okay then, what results are most relevant to the philosophy of mathematics? Oct5 comment What mathematical questions or areas have philosophical implications outside of mathematics? @Carl, @Americo: I decided to exclude the philosophy of mathematics itself as it would probably be better dealt with in a separate question Sep14 comment Terminology for handling probabilities with partial knowledge @T: I was asking for terminology to make it clear that a certain probability was based on the knowledge that a particular individual posessed, rather than the complete knowledge available from the question. I am using simply "probability" to refer to the probability from our perspective Sep11 comment Terminology for handling probabilities with partial knowledge @whuber: There is no need to apologise - I wanted it as an answer so that I could accept it Sep10 comment Terminology for handling probabilities with partial knowledge @Kaestur: Updated question. @whuber: I think that is the answer. Do you want to post it as an answer? Sep8 comment Terminology for handling probabilities with partial knowledge That isn't quite it Sep3 comment What's more general than category theory? We can also go more general. The question is, how useful will it be?