This paper presents a pure recursive definition of the positive integers in the language of pure equality, whose only non-logical symbol is the identity predicate \(=\). Beginning with the base case \(\mathbf{1}\) (existence with no distinction) and \(\mathbf{2}\) (the first emergence of distinction), each higher number \(\mathbf{n}\) is defined inductively: for every object in an \(\mathbf{n}\)-object collection, there are precisely \(\mathbf{(n-1)}\) other objects that differ from it. This construction shows that it is not necessary to define ``exactly \(n\)'' through syntactically complex formulas whose length grows with \(n\) and presupposes meta-linguistic counting. Instead, it relies solely on the primitive notions of existence, identity, and distinction. A direct proof that \(1 + 1 = 2\) is given using only the primitives of identity and distinction. The recursive definition respects the proper direction of explanation—from the simpler to the more complex—and reveals the positive integers as successive degrees of distinctions.