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| bio | website | |
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| location | ||
| age | ||
| visits | member for | 6 months |
| seen | Nov 17 '12 at 14:12 | |
| stats | profile views | 2 |
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Nov 17 |
comment |
$f,g:[a,b]\to [a,b]$ are continuous, $f\circ g=g\circ f$ and $f$ is 1-1. Show that $\exists t\in [a,b]$ so that $f(t)=g(t)=t$ But how do I know $(t_n)$ converges? And I am certain limits of sequences are not required for the solution of this homework problem |
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Nov 17 |
comment |
$f,g:[a,b]\to [a,b]$ are continuous, $f\circ g=g\circ f$ and $f$ is 1-1. Show that $\exists t\in [a,b]$ so that $f(t)=g(t)=t$ So all $t_i$ are fixed points of $g$. But I need to choose one so that $f(t_i)=t_i$. But by your construction, $f(t_{i})=t_{i+1}$... |
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Nov 17 |
awarded | Student |
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Nov 17 |
asked | $f,g:[a,b]\to [a,b]$ are continuous, $f\circ g=g\circ f$ and $f$ is 1-1. Show that $\exists t\in [a,b]$ so that $f(t)=g(t)=t$ |
