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 Sep 26 reviewed Approve A question about compactness and separability with respect to box and product topology Sep 24 awarded Popular Question Sep 24 comment Prove that $2^n>n^4$ for all $n\geq 17$ It genuinely seems like these types of problems come easy with an inordinate amount of practice, and having knowledge of general techniques. I would have never considered many of those inequalities. Sep 24 asked Prove that $2^n>n^4$ for all $n\geq 17$ Sep 24 awarded Custodian Sep 24 asked Direct proof of the existence of Strong Induction using the Well Ordering Principle Sep 22 accepted Prove that $(\mathbb{R}\setminus \{0\},\sim):= ab>0$ is transitive. Sep 22 accepted Determine whether the function $\alpha:A\times B\rightarrow B\times A$ where $\alpha((a,b))=(b,a)$ is injective and/or surjective Sep 22 accepted Give an example of two functions $\alpha,\beta$ on a set $A$ such that $\alpha\circ\beta=\mathsf{id}_{A}$ but $\beta\circ\alpha\neq\mathsf{id}_{A}$. Sep 22 accepted Proving that $\alpha:\mathbb{R}\to\mathbb{R}$ where $\alpha(x)=\frac{x^{3}}{x^{2}+1}$ is bijective Sep 22 comment Proving that $\alpha:\mathbb{R}\to\mathbb{R}$ where $\alpha(x)=\frac{x^{3}}{x^{2}+1}$ is bijective I'm afraid that goes way beyond my understanding at this level... I was warned by my prof that trying to find an inverse may end up being too messy, so you've just proven that for me... Sep 22 comment Proving that $\alpha:\mathbb{R}\to\mathbb{R}$ where $\alpha(x)=\frac{x^{3}}{x^{2}+1}$ is bijective I don't follow how you converted $x^2+xy+y^2$ as $\frac{3}{4}(x+y)^2+\frac{1}{4}(x-y)^2$ Sep 22 comment Proving that $\alpha:\mathbb{R}\to\mathbb{R}$ where $\alpha(x)=\frac{x^{3}}{x^{2}+1}$ is bijective This seems very strange to me, claiming that it is injective under the constraint that $x=y=0$. Shouldn't $x=y$ no matter what? Sep 22 asked Proving that $\alpha:\mathbb{R}\to\mathbb{R}$ where $\alpha(x)=\frac{x^{3}}{x^{2}+1}$ is bijective Sep 21 comment Give an example of two functions $\alpha,\beta$ on a set $A$ such that $\alpha\circ\beta=\mathsf{id}_{A}$ but $\beta\circ\alpha\neq\mathsf{id}_{A}$. I was fixated on finite sets.. this is why I was confused. Sep 21 asked Give an example of two functions $\alpha,\beta$ on a set $A$ such that $\alpha\circ\beta=\mathsf{id}_{A}$ but $\beta\circ\alpha\neq\mathsf{id}_{A}$. Sep 21 revised How many reflexive and symmetric relations are in set $A$? added 35 characters in body Sep 21 asked How many reflexive and symmetric relations are in set $A$? Sep 20 comment Determine whether the function $\alpha:A\times B\rightarrow B\times A$ where $\alpha((a,b))=(b,a)$ is injective and/or surjective @SpamIAm I suppose I missed a step. I intended to say $(b,a)=(d,c)$ as these are the images of $(a,b)$ and $(c,d)$. Sep 20 revised Determine whether the function $\alpha:A\times B\rightarrow B\times A$ where $\alpha((a,b))=(b,a)$ is injective and/or surjective edited body