The field axioms from the last episode are not enough in order to have a good enough basis to do analysis. A striking fact underlining this lack of definedness can be seen in that the field consisting of 0 and 1 only is fine with the field axioms and surely does not contain the natural numbers. So what's the fix then? We introduce the existence of positive elements. These positive elements are closed under multiplication and addition and obey the rule that any real number is exactly one of the three alternatives it is either positive, zero or its negative is positive. With these properties we can show seemingly obvious statements like 1 is positive. Note that only with the field axioms such a conclusion cannot be made. So we need the order axioms. Finally, this will eventually also suffice to find the natural numbers as a subset of the reals, which is the main theorem of this episode.