I am trying to find a smooth and differentiable function, which converges to the characteristic function $\mathbf{1}_{[a,b]}$. Is there an easy idea how to realise that? I suppose it should look like this $$ f_n(x)= \left\{ \begin{array}{ll} 1 & x \in [a,b] \\ 1-n(x-b) & \, x\in [b,(1/n)+b] \\ n(...
In Intro Number Theory a key lemma is that if $a$ and $b$ are relatively prime integers, then there exist integers $x$ and $y$ such that $ax+by=1$. In a more advanced course instead you would use the theorem that the integers are a PID, i.e. that all ideals are principal. Then the old lemma can...
I would like to propose a new tag: Math art. In my browsing I have found some questions like this 1 , 2 etc whose point is to create art from mathematical expressions. I think encouraging such questions and creating said tag would add another positive dimension to the site. What do you people thi...
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