These two questions would certainly deserve better (more descriptive) titles, although I was not able to come up with one.) And perhaps they could be closed as duplicates.
They both ask about the same result, the only difference is that one of them although suggests a counterexample. But in the comments it is explained that the counterexample does not work.
Suppose $f(x)$ and $g(x)$ are continuous functions on $[a,b]$ with $f$ monotone increasing. Assume there exists a sequence $x_n \in [a, b]$ such that for all $n \in \mathbb{N}$ , $g(x_n) = f(x_{n+1})$. Show that there exists $x_0 \in [a,b]$ such that $g(x_0) = f(x_0)$.
Just wondering if this que...
Suppose f(x) and g(x) are continuous functions on [a,b] with f monotone increasing. Assume there exists a sequence $x_n \in [a, b]$ such that for all $n \in N$ , $g(x_n) = f(x_{n+1})$. Show that there exists $x_0 \in [a,b]$ such that $g(x_0) = f(x_0).$
Can someone provide an example of a functio...
However I cannot vote to close as: This question does not have an upvoted or accepted answer.
(Another possibility would be leaving one question answered with the proof of that result, and in the other question post explanation why the suggested counterexample does not work as an answer.)
The problem is to show how to construct a cubic graph of v vertices whenever v is even. (for v $\ge4$)
I think I'm supposed to use a degree sequence to aid my construction, but I need help getting started.
The problem is to show how to construct a cubic graph of v vertices whenever v is even. (for v $\ge4$)
I think I'm supposed to use a degree sequence to aid my construction, but I need help getting started.
