Hagen von Eitzen
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397/400 score
 9h answered Show that $f(n)$ is $O(g(n))$ then $f(n)+c$ is $O(g(n))$ 9h comment Find all functions f such that $f(f(x))=f(x)+x$ There's no need to assume surjectivity. Injectivity follows readily and your $(4)$ for $a,b>0$ shows (using continuity) that $[0,\infty)$ is in the image. As $x\mapsto-f(-x)$ also has the given property, we conclude that also $(-\infty,0]$ is in the image. (This also shows we need only consider $a>0$) 9h comment Find all functions f such that $f(f(x))=f(x)+x$ Pfft, continuous is lame. ;) 10h comment Proving that $a^{b}$ is rational (Elementary number theorey) I hate to tell this, but your argument is almost totally unrelated to the claim, as it begins with an erroneous contraposition 10h comment When can a set have an upper bound but no least upper bound? Try $\emptyset$ 12h comment Find all functions f such that $f(f(x))=f(x)+x$ These should be all $\mathbb Q$-linear solutions. My solution set overlaps with @Michael's, but neither solution set is contained in the other. 12h answered Find all functions f such that $f(f(x))=f(x)+x$ 13h comment Can math be subjective? like this, not like this. Of course the method is the same, but I really have difficulties "to adapt my eyes" 13h comment Show that from a group of seven people whose (integer) ages add up to 332 one can select three people with the total age at least 142. This is in fact a nice idea, but I think one needs a bit more care to elaborate such an "equilibrum" argument to work with several resdistribution steps. At which moment you certainly exceed thet complexity of Barry Cipra's argument. 13h comment Limit of sequence of real numbers monotone is not needed, $m(n)\to\infty$ should be enough (and would possibly match the OP's notion "$m\to\infty$ as $n\to\infty$") 1d awarded Good Answer 1d comment Prove sequence ${x_{n + 1}} = \sin {x_n},{x_1} = 1$ has a limit @Henry It's ok if hints are just hints and not complete :) 1d comment Does there exist a function $g\in \mathbb{N}^\mathbb{N}$ s.t. $\{f\circ f=g\}$ is not empty and finite? @Riley there are continuum-many $f$ in that case: Map any subset $A$ of $\mathbb N$ to $0$, map the rest somewhere into $A$. 1d answered Let $A\in \mathbb C$ be a $2 \times 2$ matrix, let $f(x)=a_0+a_1x+\cdots a_nx^n$ be any polynomial over $\mathbb C$. Comment on $f(A)$ 1d answered Can a set containing a string of length $\omega_0$ be well-ordered by substring total order? 1d awarded exponentiation 2d revised Is it impossible to recover multiplication from the division lattice categorically? edited body 2d comment Is there some connection between the killing form and a killing vector field? @snulty A fact which too me long to grasp (ah, it makes something zero, that's why its called killing form - oh wait, why do they keep writing Killing form?) 2d comment Definition of homeomorphic? Note that 1. is in fact the literal translation of homeo (ὅμοιος - equal, similar) morph (μορφή - form, shape) ic 2d comment Will $x=0$ satisfy the equation $\sqrt{\tan(3x)}=\sqrt{-\tan(x)}$? As this problem seems to come from a "central exam" of the well-known Lomonossov University, it is really a shame that one of the solutions is missing.