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haya
 Post subject: i need counter example for each one of the follwing
PostPosted: Fri, 1 Apr 2011 10:50:32 UTC 
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outermeasure
 Post subject: Re: i need counter example for each one of the follwing
PostPosted: Fri, 1 Apr 2011 11:08:55 UTC 
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haya wrote:
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Where is your work?

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\begin{aligned} Spin(1)&=O(1)=\mathbb{Z}/2&\quad&\text{and}\\ Spin(2)&=U(1)=SO(2)&&\text{are obvious}\\ Spin(3)&=Sp(1)=SU(2)&&\text{by }q\mapsto(\mathop{\mathrm{Im}}\mathbb{H}\ni p\mapsto qp\bar{q})\\ Spin(4)&=Sp(1)\times Sp(1)&&\text{by }(q_1,q_2)\mapsto(\mathbb{H}\ni p\mapsto q_1p\bar{q_2})\\ Spin(5)&=Sp(2)&&\text{by }\mathbb{HP}^1\cong S^4_{round}\hookrightarrow\mathbb{R}^5\\ Spin(6)&=SU(4)&&\text{by the irrep }\Lambda_+\mathbb{C}^4 \end{aligned}
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haya
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PostPosted: Fri, 1 Apr 2011 11:12:32 UTC 
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for (ii) I think f(x)=x^2 -4 on [-5,5], f(x)=0, f(-5).f(5)>0, f(x)=0,
x=-or+2 which is on [-5,5]

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aswoods
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PostPosted: Sat, 2 Apr 2011 02:58:24 UTC 
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(ii) Correct
(iii) Consider x³
(iv) Consider g(x)=x²
(v) Which definition...?
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