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 Dec20 revised Could “$\infty$” be understood by taking the reciprocals of the Hyperreal numbers? deleted 38 characters in body Dec20 asked Could “$\infty$” be understood by taking the reciprocals of the Hyperreal numbers? Dec19 awarded Constituent Dec16 comment Is the derivative of $\{x\}$ on $(0,1)$ always equal to $1$? Yes, sorry - question updated. Thanks for spotting this. Dec8 awarded Caucus Dec7 awarded Nice Answer Dec3 comment Summation of logarithms You have $$S=\sum_{k=1}^n\log(a-x_k)=\log\prod_{k=1}^n(a-x_k).$$ So $$\prod_{k=1}^n(a-x_k)-e^S=0.$$ So you need to be able to solve equations of the form: $$\prod_{k=1}^n(a-x_k)-c=0,$$ where $c$ is some constant. Nov26 awarded Notable Question Nov20 comment Finding the roots of $x^2+(3+5i)x+(7+11i)=0$ Re polar exponential form - see my answer below for the answer. Nov20 revised Finding the roots of $x^2+(3+5i)x+(7+11i)=0$ added 542 characters in body Nov20 revised Finding the roots of $x^2+(3+5i)x+(7+11i)=0$ added 542 characters in body Nov20 answered Finding the roots of $x^2+(3+5i)x+(7+11i)=0$ Nov19 comment Most ambiguous and inconsistent phrases and notations in maths Since I used $\log$ instead of $\text{Log}$ and I did not specify a branch then to me this is clearly a mistake. Nov19 comment Most ambiguous and inconsistent phrases and notations in maths @Mariano Suárez-Alvarez The notation $\text{Log}$ is also sometimes reserved for the principal branch, often when $\log$ for the (general) multi-valued function is used. In whichever context, I've seen this cause confusion in obtaining results. Nov15 comment What was the first bit of mathematics that made you realize that math is beautiful? (For children's book) In fact: $e^{ix}=\cos(x)+i\sin(x)$. Nov13 comment What was the first bit of mathematics that made you realize that math is beautiful? (For children's book) Good point. I think at the time I "understood" what numbers were, but these new numbers (complex numbers) were so strange, and were presented with the added "imaginary" verbiage that they were mesmerizing to me! Of course later I realised that complex numbers are not complex at all and that there is absolutely nothing imaginary about the idea of $i$. Complex numbers are a system of numbers which obey a certain set of rules in a consistent way. But I'm pleased to have been captivated :-) Nov11 comment The Integral of Multiple Tangent Functions Try increasing the working precision: Integrate[..., WorkingPrecision->100]. Nov11 revised Is the derivative of $\{x\}$ on $(0,1)$ always equal to $1$? added 311 characters in body Nov11 comment Is the derivative of $\{x\}$ on $(0,1)$ always equal to $1$? So it's down to the method used to compute the derivative. Need to be judicious with tools. Nov10 accepted Is the derivative of $\{x\}$ on $(0,1)$ always equal to $1$?