Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

For $k=2$, from this post A "geometrical" representation for Ramsey's theorem, how one can deduce the theorem from Constant $f:[\mathbb{N}]^2\to \{1,2\}$ (part 2), or by knowing that there exist infinite sequence of naturals $n_1,n_2,n_3,...$, and a sequence of $t_1,t_2,t_3,...$ where $t_n\in\{1,2\}$ for all $n$, and if $i<j$, then $f(\{n_i,n_j\})=t_i$.

How to represent set $H$ (set $H$ is from the first link)?

share|improve this question

1 Answer 1

up vote 2 down vote accepted

You’re practically done at this point.

Let $N_1=\{n_k:t_k=1\}$ and $N_2=\{n_k:t_k=2\}$. At least one of these sets must be infinite, so without loss of generality assume that $N_1$ is infinite; then $f(\{n_i,n_k\})=1$ for all $\{n_i,n_k\}\in[N_1]^2$.

share|improve this answer

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.