I’m doing something that I should have done a long time ago: collecting a series of posts into one single post. The following links comprised my series on adding by a form of 0 (analogous to multiplying by a form of 1).
Part 1: Introduction.
Part 2: The Product and Quotient Rules from calculus.
Part 3: A formal mathematical proof from discrete mathematics regarding equality of sets.
Part 4: Further thoughts on adding by a form of 0 in the above proof.