Editing Surreal number (section)

====Birthday property====
A form {{math|1=''x'' = {{mset| ''L'' {{!}} ''R'' }}}} occurring in generation {{mvar|n}} represents a number inherited from an earlier generation {{math|''i'' < ''n''}} if and only if there is some number in {{math|''S''{{sub|''i''}}}} that is greater than all elements of {{mvar|L}} and less than all elements of the {{mvar|R}}.  (In other words, if {{mvar|L}} and {{mvar|R}} are already separated by a number created at an earlier stage, then {{mvar|x}} does not represent a new number but one already constructed.)  If {{mvar|x}} represents a number from any generation earlier than {{mvar|n}}, there is a least such generation {{mvar|i}}, and exactly one number {{mvar|c}} with this least {{mvar|i}} as its birthday that lies between {{mvar|L}} and {{mvar|R}};  {{mvar|x}} is a form of this {{mvar|c}}. In other words, it lies in the equivalence class in {{math|''S''{{sub|''n''}}}} that is a superset of the representation of {{mvar|c}} in generation {{mvar|i}}.