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 Oct 10 comment I don't understand why we represent functions $f:I \subseteq \Bbb R \to \Bbb R^2$ the way we do. Also note that for 1-argument functions the image is usually just an interval on the real line, not an interesting set. For this reason interesting images (such as parametric curves) usually appear for 2-argument (or more arguments) functions. This was the exact reason of your confusion, when you switched from 1-argument to 2-argument functions Oct 10 answered I don't understand why we represent functions $f:I \subseteq \Bbb R \to \Bbb R^2$ the way we do. Oct 10 asked Locally monotone function is monotone Oct 9 answered Another conjecture about $C^1$ integral curves Oct 8 comment Another conjecture about $C^1$ integral curves Probably we can build a counter-example based on $f(x) = \begin{cases}x^2\sin{(\tfrac{1}{x})} & \mbox{if }x \neq 0, \\ 0 &\mbox{if }x = 0\end{cases}$ from en.wikipedia.org/wiki/Smoothness Oct 8 comment Prove (in an abstract setting) that a function is right differentiable and the right derivative is continuous Another similar conjecture: math.stackexchange.com/questions/1470877/… Oct 8 asked Another conjecture about $C^1$ integral curves Oct 8 revised Prove (in an abstract setting) that a function is right differentiable and the right derivative is continuous edited body Oct 8 answered Prove (in an abstract setting) that a function is right differentiable and the right derivative is continuous Oct 8 revised Prove (in an abstract setting) that a function is right differentiable and the right derivative is continuous edited tags Oct 8 revised Prove (in an abstract setting) that a function is right differentiable and the right derivative is continuous added 7 characters in body Oct 8 revised Prove (in an abstract setting) that a function is right differentiable and the right derivative is continuous added 92 characters in body Oct 8 revised Prove (in an abstract setting) that a function is right differentiable and the right derivative is continuous [Edit removed during grace period] Oct 8 revised Prove (in an abstract setting) that a function is right differentiable and the right derivative is continuous edited body Oct 8 asked Prove (in an abstract setting) that a function is right differentiable and the right derivative is continuous Oct 6 accepted Two ways to describe image of a filter under a function Oct 6 comment Two ways to describe image of a filter under a function "minus" -> "minutes" in my previous comment Oct 6 comment Two ways to describe image of a filter under a function Hm, I spent around ten minus trying to prove this, yet without success. I expected it to be easier. Any proof (not only the shortest one) would be helpful Oct 6 comment Two ways to describe image of a filter under a function I wonder that Google for ("filter image" | "image of filter") function set "filter base" does not find relevant enough results Oct 6 asked Two ways to describe image of a filter under a function