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 Feb 6 awarded Yearling Mar 30 answered How do I show $SO(n)$ is open and closed in $O(n)$? Mar 30 answered 8 / 4 (4-2) = ? What is answer? Mar 30 comment Does $(a)=(b)$ imply that $a$ and $b$ are associate in a principal ideal ring? Usually people talk about $PID$, principal ideal domains. These are integral domains, so from $a=xb$ and $b=ya$ you can establish that $a(1-xy)=0$ so that indeed $x,y$ are units. Is there any reason to study non-domains? Mar 30 comment If $f$ is a increasing function in $[a,b]$, then is it true that $\text{Img}(f) = [f(a),f(b)]$? Not quite - I prefer left continous functions :-) Mar 30 answered If $f$ is a increasing function in $[a,b]$, then is it true that $\text{Img}(f) = [f(a),f(b)]$? Mar 26 comment Application of Inverse Function Theorem No, it is ok - formal enough and correct. I just wanted to show you another point of view. Mar 26 answered Application of Inverse Function Theorem Mar 25 answered How to prove that the tangent to a circle is perpendicular to the radius drawn to the point of contact? Mar 23 revised Verify that Log$(z^{w}) = w$Log$z$ + $2\pi i n$ deleted 44 characters in body Mar 23 answered Verify that Log$(z^{w}) = w$Log$z$ + $2\pi i n$ Mar 12 revised How to explain the formula for the sum of a geometric series without calculus? added 431 characters in body Mar 12 answered How to explain the formula for the sum of a geometric series without calculus? Mar 10 answered Paradox: Is $1 \in (0,1)$? Mar 9 answered Mass of a thin wire given density Mar 9 answered Prove $(a + b)^2 \geq 4ab$ Mar 6 answered Why use open sets in definitions? Mar 6 revised Show that: $(i) M \cong N$ and $G/M \cong G/N$ >or >$(ii) M \cong G/N$ and $G/M \cong N$ added 152 characters in body Mar 5 answered Show that: $(i) M \cong N$ and $G/M \cong G/N$ >or >$(ii) M \cong G/N$ and $G/M \cong N$ Mar 2 comment Prove that $\mathbb{R}^p \backslash\{ a_1,a_2,\dots,a_n \}$ is open another trick is $f(x)=\prod |x-a_i|$, what is $f^{-1}(\mathbb{R}\setminus \{0\})$