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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 $f^{-1}(\mathbb{R}\setminus \{0\})$
Feb
27
comment let G be a group, and H is a subgroup. The number of elemens is half of the element of G
$H$ is normal, think about $\bar{x}$ in $G/H$