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# 211 Comments

 Aug 31 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? Jun 1 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 Mar 15 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) Mar 15 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 Nov 1 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 Jul 25 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. Apr 10 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! Nov 25 comment What are the Axiom of Choice and Axiom of Determinacy? Did you mean f(p(x))=x for equivalent 3? Apr 16 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 Apr 15 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) Dec 15 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 Dec 15 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? Oct 6 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 Oct 5 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? Oct 5 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 Sep 14 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 Sep 11 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 Sep 10 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? Sep 8 comment Terminology for handling probabilities with partial knowledge That isn't quite it Sep 3 comment What's more general than category theory? We can also go more general. The question is, how useful will it be?