# Question about a Ramsey graph.

1. Dec 30, 2012

### cragar

the Ramsey number of $R(\omega,\omega)=\omega$
but then $R(\omega+1,\omega)=\omega_1$
My question is on the second one can we do a counter example to show that it cant
be any countable ordinal.
depending on how I count the natural numbers I can get any countable ordinal I want.
If we assume that $R(\omega+1,\omega)$ was equal to some countable ordinal
then I could just color $\omega$ edges with blue for example and i would stay
under the $\omega+1$ limit . And the other color we would just use a finite number of them.
I guess i don't really understand why order matters for an infinite Ramsey graph.
It doesn't seem like it matters in the finite case.