Ascending order is just one of many arbitrary orders. An ordering is a first output of a generator function, a second output, a third output, etc, where for any

Ascending order is just one of many arbitrary orders. An ordering is a first output of a generator function, a second output, a third output, etc, where for any arbitrarily chosen element X of the set (such as the positive integers or reals), we can show that the generator will reach X in N steps, for some finite N. That is why ascending order is the norm for the positive integers. For any positive integer X, it is clear that we will reach it in X steps using that generator function. So, it’s not a matter of being mainstream, it’s just the simplest. The difference between the infinity of the reals and the positive integers is that there is no such generator function for the reals. No matter what function you give me, I can write a finite number that you will not reach in a finite number of steps. Feel free to give me a generator function and I will give you a finite number that it cannot reach in finite steps. On the other hand, try giving me a finite positive integer that I cannot reach in finite steps.