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 Apr 8 awarded Good Question Apr 5 asked If $N=aP+R$ and $P=bQ+S$, show that $\cfrac{N}{ab}=aS+R$? Apr 5 answered Why $h\phi (x)$ is analog to $\frac{\partial f}{\partial x}h+ \frac{\partial f}{\partial y}k$? Apr 3 asked Why $h\phi (x)$ is analog to $\frac{\partial f}{\partial x}h+ \frac{\partial f}{\partial y}k$? Mar 26 awarded Popular Question Mar 21 awarded Good Question Mar 19 comment Find two matrices $A,B$ such that $AB=0, BA\neq 0$. What can you say about $(BA)(BA)$? I made a typo, corrected it now (while laughing for a bit.) Mar 19 revised Find two matrices $A,B$ such that $AB=0, BA\neq 0$. What can you say about $(BA)(BA)$? edited body; edited title Mar 19 asked Find two matrices $A,B$ such that $AB=0, BA\neq 0$. What can you say about $(BA)(BA)$? Mar 16 comment If $A,B$ are invertible, show that $AB$ is invertible and express $(AB)^{-1}$ in terms of $A^{-1},B^{-1}$. @Roland Yes. You ask "How to calculate the determinant and make orange juice with it?" and "How to calculate the determinant?" and people think it is a duplicate. Mar 16 comment If $A,B$ are invertible, show that $AB$ is invertible and express $(AB)^{-1}$ in terms of $A^{-1},B^{-1}$. @JMoravitz I've read a book on fallacies: "Fallacies and argument apraisal". In it, the author argues that we ended up teaching people that fallacies are bad and must be avoided but it's actually not that simple because in a deeper study, one can observe that there are situations in which fallacies work, that is, are not actually fallacies. I believe the same could be asked on circular logic: Is it always bad? In this case, it helped me yield the correct answer. Is it really a devil that must be avoided at all costs and there are no occasions in which it could be helpful? Mar 16 revised If $A,B$ are invertible, show that $AB$ is invertible and express $(AB)^{-1}$ in terms of $A^{-1},B^{-1}$. added 376 characters in body Mar 13 comment Is it possible to prove uniqueness without using proof by contradiction? But then, we usually have to prove the uniqueness. Isn't "suppose there are two" (without the different) a contradiction towards the uniqueness? Mar 13 comment Is it possible to prove uniqueness without using proof by contradiction? I don't get it. Aren't you imposing the uniqueness instead of proving it? You say that if there are $x,y$ such that $\phi (x)$ and $\phi (y)$, then they are the same. This seems more that you're forcing it to be that way instead of showing it as a consequence of some earlier assumption. Mar 13 comment Is it possible to prove uniqueness without using proof by contradiction? @DavidZ I know those aren't proofs. C'mon, I'm stupid but not all that stupid you're expecting. Mar 13 asked What is the meaning of “perceiving all sets”? Mar 13 comment Is it possible to prove uniqueness without using proof by contradiction? @CliveNewstead The empty set, the real numbers zero and one. (Does that answer apropriately?) Mar 13 comment Is it possible to prove uniqueness without using proof by contradiction? @CarlMummert Weird. It's often presented as: "Suppose there are two..." - and it really seems a contradiction. Mar 13 revised Is it possible to prove uniqueness without using proof by contradiction? edited tags Mar 13 asked Is it possible to prove uniqueness without using proof by contradiction?