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8h
revised Is the polynomial $x^3 + 2x^2 + 1$ irreducible in $\mathbb{Z}_{17}[x]$?
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19h
comment For any element $g$ of $G,$ where $g$ has order $2,$ define $gH=\{gh│h∈H\}$. Prove that the set $K=H∪gH$ is a subgroup of $G.$
I have updated my answer to address your second proof attempt. Take a look, and let me know if you have any questions.
19h
revised For any element $g$ of $G,$ where $g$ has order $2,$ define $gH=\{gh│h∈H\}$. Prove that the set $K=H∪gH$ is a subgroup of $G.$
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21h
revised If $\inf A < 1 $ …?
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1d
comment For any element $g$ of $G,$ where $g$ has order $2,$ define $gH=\{gh│h∈H\}$. Prove that the set $K=H∪gH$ is a subgroup of $G.$
Nope. The only element whose order we've made any assumption about is $g$. What have you done/tried so far in your proof? Please feel free to add your proof attempt to your post, and I'll look through it (in the morning, after I've slept).
1d
comment For any element $g$ of $G,$ where $g$ has order $2,$ define $gH=\{gh│h∈H\}$. Prove that the set $K=H∪gH$ is a subgroup of $G.$
Exactly right! How goes the proving?
1d
revised What can you say the upper or lower bound of $P(A\cup B)$ and $P(A\cap B)$
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1d
revised Let $X = [0,2]$ and $A = \{0,1,2\}$. Prove that $X / A$ is homeomorphic to $C_{1}$ ∪ $C_{-1}$
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1d
comment Sequences and series and what is good enough
@Paul: Belatedly, I realized that I was incorrect about the important point, and why your approach doesn't work. Consider instead the series $$\sum_{n=1}^\infty\frac1{n^2+n^{-2}}.$$ This readily satisfies $2+-2<1$ and $\min\{2,-2\}<1,$ and yet it converges! In my comments above, I should have used $\max$ instead of $\min$.
1d
comment Finding the limit of a function 5
Duplicate of this question.
1d
revised Roots of $x^2+3x+2=0$ are infinite !!!
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1d
comment Is it possible that $(f\circ g)(x)=x$ and $(g\circ f)(x)\ne x$?
That's a good point. I really shouldn't post before I have my coffee. -___-
1d
revised Is it possible that $(f\circ g)(x)=x$ and $(g\circ f)(x)\ne x$?
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1d
answered Is it possible that $(f\circ g)(x)=x$ and $(g\circ f)(x)\ne x$?
2d
revised How can the axioms (and primitives) of Tarski's axiomatization of $\Bbb R$ be independent?
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2d
asked How can the axioms (and primitives) of Tarski's axiomatization of $\Bbb R$ be independent?
2d
comment Why were space filling curves found to be counterintuitive?
The difference is that fabric is made of space-filling thread.
Apr
30
revised Does $1^i$ and $1^{\frac{0}{0}}$ also give $1$ again?
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Apr
30
comment Does $1^i$ and $1^{\frac{0}{0}}$ also give $1$ again?
But $\frac00$ isn't a number, so what would it even mean to talk about $1^\frac00$?
Apr
30
answered Invariant subspaces of the identity map