Sequencing is Ordering in Ranking determined by Value, Predecessor or Successor, Catalyst or Response, and Associative and/or Commutative Properties. 

I will be blunt, the only common denominator I can find as to *why* we have an Order of Operations is due to the Logical Order of Disintegration/Integration.

The reason why we have Sequence is to Communicate “who” is dependent on “who” and “who” has components of the Elder placement and who does not in the same way that a Grandfather has 0 Components of his Son and Grandson, but a Son has 1  Grandfather Component while the Grandson has 2 “Grandfather Components,” which is why they are in the oder of 0,1, and 2 or “Grandfather,” “son,” and “grandson.”

This is called “Hierarchy.” pronounced HERE-ar-chee — and moves always from Left to Right to honor “Fleming’s Left Hand Law” in Physics. 

Be sure you pronounce this word with three Syllables and not four.

This Order and Sequence is the assignment of “Origin,” “Independent” and “Dependent.”

This is Logic.