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 May 14 reviewed Approve Why does $\sin(0)$ exist? May 14 comment Discrete Laplace Tranform. I asked a similar question here: math.stackexchange.com/questions/793550/… - what I find strange though is that while you can also read that the Laplace transform is the continuous analog of the dot product for infinite dimensional vectors (=functions) you still calculate infinitely many terms in the discrete version (and not just over the available dimensions of your vectors as with the dot product) - perhpas you could contribute :-) May 14 comment Discrete Laplace Tranform. I asked a similar question here: math.stackexchange.com/questions/793550/… - what I find strange though is that while you can also read that the Laplace transform is the continuous analog of the dot product for infinite dimensional vectors (=functions) you still calculate infinitely many terms in the discrete version (and not just over the available dimensions of your vectors as with the dot product) - perhpas you could contribute :-) May 14 comment Example for finite dimensional analog of integral transforms @MattL.: Thank you, what still bothers me with this finite version is that the sum is over infinitely many terms because the dot product is only over the available dimensions. May 13 reviewed Approve Trigonometric substitution May 13 comment Example for finite dimensional analog of integral transforms @MattL.: I had a quick look at it and it looks promising - so first thank you! Could the $z$ also be real valued like e.g. $2$? May 13 comment Example for finite dimensional analog of integral transforms @MattL.: To be honest with you I don't know because I don't know the Z-transform well enough. But perhaps you could give an example that contains the elements I asked for in my question? May 13 asked Example for finite dimensional analog of integral transforms May 9 awarded Notable Question Apr 28 awarded Nice Question Apr 28 revised Intuition for complex eigenvalues edited title Mar 9 accepted Intuition and counterexamples for higher-order derivative test Mar 8 comment Intuition and counterexamples for higher-order derivative test I was just talking about your example: In our axiomatic system it is not defined at point $0$ because you are dividing by zero there! I am not talking about nature but only about things happening within the realms of pure maths. Yet could you give me a reference for the number of smooth functions and formulas accessible? Thank you again. Mar 8 comment Intuition and counterexamples for higher-order derivative test The intuition is appealing - thank you and +1! Considering your example: I disagree: It does not have a minimum at zero - it has literally nothing at zero because it is not defined there, neither are any of its derivatives (see also comments to my question). Mar 8 comment Intuition and counterexamples for higher-order derivative test Is it possible to find a counterexample where you don't have a separate case at the extreme value (as with this example at $0$)? This feels a little bit like cheating because the "original function" is not defined at this point. Mar 8 comment Intuition and counterexamples for higher-order derivative test Thank you Daniel: $x^{12}$ doesn't answer my question concerning an intuition. Even $x^4$ would work as an example, this is not the problem. Mar 8 asked Intuition and counterexamples for higher-order derivative test Feb 25 reviewed Approve How do I solve $y'=\frac{y}{x}\frac{x-y}{x+y}$? Feb 25 reviewed Approve Integral equation and constant rules Feb 25 reviewed Approve Factoring $x$ out of the denominator of a limit