User blog comment:WaxPlanck/Chess Ordinals and Uncountable Growth/@comment-32783837-20180122235118/@comment-32876686-20180123000709

Because the supremum of all values for n-th dimensional chess, (even if n is a countably infinite value), is \(\Omega\), or \(\omega_1\), and therefore it does not make a difference how many dimensions there are. (Provided of course the squiggly mark underneath the \(\mathfrak{Ch}\) is meant to imply that there an infinite number of pieces on the 'board'.