26 reputation
1
bio website
location
age
visits member for 2 years, 1 month
seen Nov 17 '12 at 14:12

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
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, $f(t_{i})=t_{i+1}$...
Nov
17
awarded  Student
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 $f(t)=g(t)=t$