is the unique object in whichever complete ordered field you have selected, that happens to be positive and to square to the number 2 in that field, where 2 is the number 1 + 1 in that field, where 1 is the unique multiplicative identity in that field. This is the structural role played by . In any complete ordered field, every rational number is algebraically definable, and every real number is characterized by the cut that it makes in the rational numbers. It follows that the real field ℝ is a Leibnizian structure: any two real numbers are discernible in the language of fields.
