File:Surreal less than or equal to.svg

The asterisk on <* is used to distinguish this inequality from the familiar version of <. The <* is required for sets of numbers: If x is any real number, and { } is the null set, a<*{ } is taken to be a true statement. In other words, 3≥{ } cannot be true because it is meaningless to compare a number with a non-number. This permits us to define a modified "converse" statement 3<*{ } to be true! Incidentally, the equivalence of a<b to b≥a remains true if a and b are either real or surreal numbers. For more information, visit https://www.tondering.dk/download/sur.pdf

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