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 Mar 4 suggested approved edit on What is the solution of cos(x)=x? Mar 4 comment What is the solution of cos(x)=x? What's the point of arguing it is trancedential? Fixed point of the exponent is also transcedential, but can be expressed with an integral, for instance. Mar 2 comment Does a non-trivial solution exist for $f'(x)=f(f(x))$? @Julien this answer actually better to be on top, because it addresses exactly the issue of solving the equations of the type you proposed and also gives the exact answer in the closed form to your equation. People who follow the link consisting of your caption likely want to see the result. Mar 2 comment Does a non-trivial solution exist for $f'(x)=f(f(x))$? @Julien I expected you to accept my answer because it gives you the exact answer. Mar 1 answered Does a non-trivial solution exist for $f'(x)=f(f(x))$? Feb 28 revised Closed form solution to $\frac{1}{a-1}= \log a$ added 36 characters in body Feb 28 asked Closed form solution to $\frac{1}{a-1}= \log a$ Feb 21 comment Why formal power series are not considered a system of hypercomplex numbers? LOL who said you composition of functions should be multiplication? What hypercomplex system is built this way? Feb 19 revised Why formal power series are not considered a system of hypercomplex numbers? deleted 12 characters in body Feb 5 answered Is there a general formula for solving 4th degree equations? Feb 5 comment Are there divergent series that cannot be summed up by any method? @Jack D'Aurizio are u sure it will not be convergent for any methods listed on the wikipedia's page? Feb 5 comment Are there divergent series that cannot be summed up by any method? @Jack D'Aurizio so what's the point? Feb 5 asked Are there divergent series that cannot be summed up by any method? Feb 5 comment Divergent Series The series $\sum_{k=1}^\infty \frac{1}{k}$ can be summed up, for instance using Ramanujan's summation or Cauchy principal value. The sum will be $\gamma$, Euler's constant. Jan 24 comment Differentiable only at $x=0$ and $f'(0)>0$ The example of David Mitra satisfies the first two conditions. Jan 24 comment Differentiable only at $x=0$ and $f'(0)>0$ @user197137 the definition of derivative is $\lim_{h\to 0}\frac{f(x+h)-f(x)}h$. If it is positive, then there are infinitely many such h that $f(-h) < f(0)< f(h)$ Jan 24 comment Differentiable only at $x=0$ and $f'(0)>0$ @user197137 for the function to have positive derivative, such h should exist. Jan 24 revised Using the rules that prove the sum of all natural numbers is $-\frac{1}{12}$, how can you prove that the harmonic series diverges? added 118 characters in body Jan 24 answered Using the rules that prove the sum of all natural numbers is $-\frac{1}{12}$, how can you prove that the harmonic series diverges? Jan 24 comment Numerical system that includes the limit targets such as $0^+$, $0^-$, $1^+$ etc @ajotatxe limit will be excessive in this case, in this numerical system the function can be evaluated directly: $\sin 0^+=0^+$. You can see it as the simplifyed system of hyperreals, with $0^+$ substituted for any positive infinitesmal.