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 Nov 20 awarded Student Nov 14 comment Prove continuity of a simple polynomial @sillyme, the definition of continuity in terms of sequences says that $\forall\ x_k \rightarrow A$ you must have $f(x_k) \rightarrow f(A)$. Your goal is to prove the reverse. Hence, $\forall$ turns into $\exists$. In other words, you need only one sample to present that does not deliver equal limits. The concrete choice in my case is just a matter of convenience - we need some simple sequence that tends to the point in question. Does this answer your question? Nov 14 revised Correct terminology for polylines, their segments, knots, etc. added 20 characters in body Nov 14 comment Correct terminology for polylines, their segments, knots, etc. @HandeBruijn Thanks a lot! Not exactly numerical methods, but pure approximation theory, but it doesn't seem to make a difference. Nov 14 awarded Editor Nov 14 revised Correct terminology for polylines, their segments, knots, etc. more background information Nov 14 asked Correct terminology for polylines, their segments, knots, etc. Nov 14 answered Prove continuity of a simple polynomial Apr 16 awarded Supporter Nov 23 comment Partial derivative notation: $\left.\frac{\partial \cdot}{\partial\cdot} \right|_{u=T}$ The short answer is: because $T$ is the function argument, that is, considered constant in the RHS; but you can only differentiate w.r.t. independent variable. For example, put you want $f(t,5)$. The RHS becomes meaningless. Nov 22 awarded Teacher Nov 22 answered Partial derivative notation: $\left.\frac{\partial \cdot}{\partial\cdot} \right|_{u=T}$