# Definitions > [!NOTE] Definition 1 > For all $k,l\in\mathbb{N}^{+},$ $R(k,l)$ denotes the smallest positive integer so that any graph with $R(k,l)$ vertices has a $k$-clique or an independent set of $l$ vertices (that is, a set of vertices so that no pair are adjacent or equivalently, a clique in the graph's complement). > [!NOTE] Definition 2 > >[[Edge Colouring]]. > [!Example] > For all $k,$ $R(1,k)=R(k,1)=1$ since every non-empty simple graph a has an independent set of $1$ vertex and a $1$-clique. # Properties By [[Ramsey Numbers on Two Colours is Symmetric]], for all $k,l\in \mathbb{N}^{+},$ $R(k,l)=R(l,k).$ By [[Upper bound for Ramsey Numbers on Two Colours (Ramsey's Theorem)]], which guarantees their existence. # Applications