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 Apr16 comment Prove or disprove : $a^3\mid b^2 \Rightarrow a\mid b$ Your proof will work if you assume that $a^m|b^n$ and $m\geq n$. Mar3 comment Uniqueness of Solution in infinite linear programming Just out of curiosity, Is there some practical reason for solving this or is it just interesting? Feb28 awarded Yearling Jan5 comment Sum $\frac{1}{6} + \frac{5}{6\cdot 12} + \frac{5\cdot 8}{6\cdot 12\cdot 18} + \frac{5\cdot 8\cdot 11}{6\cdot 12\cdot 18\cdot 24}+\ldots$ I think that this @Ian is correct. I think that we should wait for the OP to tell us what is meant. I looked at the account of the OP and some of the questions and answers were incongruent with the type of mistake I attributed. Jan2 comment Is there a system of mathematics where everything is a function? You could use an arrows only approach to category theory. You could also look at the lambda calculus. Jan1 comment Is Russell's paradox really about sets as such? @Timbuc Many (not all) mathematicians do not really give much thought to foundations. If pressed on foundations, they may instinctively say "ZF (+/-Z) without too much thought. Even those who can name half of the axioms, much of the work can be done in many very different systems, of which ZFC is one of. So to say that most mathematicians work in ZFC might only be true in a nominal way. It may be more accurate to say that all the work one does can be carried out in ZFC (or in some occasions an extension, if one need Grothendieck universes for some things that require category theory). Dec31 comment Solving $\sqrt{x^2-5} = x-1$ It is implied in the LHS, not the RHS. On the other hand one could choose to make convection that when roots are involved in an equation (or string of equations) then the implication is propagated to the entire string. This is why I said misleading and not incorrect. When people know what they are doing, this is safe. On the other hand when people are learning, it is best to carry orotund the extra data about domains, as it will allow for quick checking of extraneous solutions. A real pedant(which I am not), however would say that $x$ is a different animal than $x,x\geq 0$. Dec31 comment Solving $\sqrt{x^2-5} = x-1$ Your hint is slightly misleading (it does not matter here, but could be good for catching extraneous solutions). It should be $(\sqrt{x})^2 , x \geq 0$. Dec31 comment Write $(1^3 −1)−(2^3 −1)+(3^3 −1)−(4^3 −1)+(5^3 −1)$ using summation or product notation. It looks complicated because you are not yet used to looking at these things. Dec30 comment Intuition for Exotic $\mathbb R^4$'s The best answers that I have heard seem to come down to low dimensional accidents. mathoverflow.net/questions/47569/… Dec28 comment Is Information Theory Mathematics? There are entire Math books written on the subject, see amazon.com/Coding-Information-Theory-Graduate-Mathematics/dp/… . Dec11 awarded Caucus Dec8 comment how to solve a linear equation with two variables? You do not have enough information to solve for both variables at the same time. You can write $$J=\frac{M}{\omega}+\frac{K}{\omega^2},$$ or $$K=\omega^2 J-\omega M.$$ Dec1 comment How to prove that nth differences of a sequence of nth powers would be a sequence of n! You should try to build a theory of "discrete differential and integral calculi" where real valued functions are replaced with sequences, the derivative is replaced with the difference operator, and the integral is replace with the summation operator. You even get an analog of the fundamental theorem of calculus. Nov30 comment Mean of standard deviation and confidence intervals Here is a way you can test this. Pick two random samples of size say ten (instead of 1000), between zero and one. Calculate the mean and standard deviations of the two examples. Then calculate the mean and standard deviation of the two samples combine and compare. Nov26 comment meaning of principal eigenvector of the normalized link matrix (pagerank) What you want to imagine is that each node has some amount of "material". At each time step, the material from each node is distributed to all of the other nodes in a way that is specified by the weighted adjacency matrix. The dominant Eigenvector then is the distribution you get after an infinite number of time steps. Oct19 comment Why can't a Venn diagram constitute a proof? It seems like you can use Venn diagrams to prove statements about subsets of $\mathbb{R}^2$ Oct19 comment Find the minimum capacity edge that is maximized among all paths from $s$ to $t$ Their are some subtleties to this. The first step is to find all the paths from $s$ to $t$, which could be infinite in number, if you graph has loops. So you would probably restrict paths that do not circle around. One you have that, it seems to me that this is a relatively straight forward search. Oct19 comment What are the continuous functions that satisfy the following? The word continuous in this case is simply an adjective you have to carry around with you during the argument. This might seem counterintuitive, but it is due to the fact that $\mathbb{R}-\{0\}$ is disconnected. Oct19 comment What are the continuous functions that satisfy the following? Minor nitpick: Based on the question, it does not seem that the question needs to be defined at zero. Of course, this does not change the character of the solution method.