--   Nimber addition is defined by \(\alpha+\beta = \operatorname{mex}\{\alpha'+\beta, \alpha+\beta'\}\).

--   Nimber addition is defined by \(\alpha+\beta = \operatorname{mex}\{\alpha'+\beta, \alpha+\beta'\}\), where \(\operatorname{mex} S\) is the smallest ordinal not in \(S\).