User blog comment:Reinhardt-C/Incremental Games with the Largest Numbers!!!/@comment-35470197-20200220231959/@comment-35470197-20200221005344

Actually, this question arised in my mind when I saw the comments below on Ordinal markup. Therefore I wondered the borderline.

For example, if given a game X to output a number does not satisfy the restrictions to admit a valid way to compute arithmetic operation, then we can create a valid game X' in which a valid expression is a formal strings like x "+" y "×" "-" z, where x, y, and z are valid expressions in X and "+", "×", and "-" are formal strings. In order to evaluate such an expression, evaluate x, y, and z and apply +, ×, and - to them. Therefore the existence of the way to compute arithmetic operation does not look the most important point in this argument.