Also, the symbol –/– calls for DIVISION.

Axiom #1.

pp/4pp –/– 2pp/2pp = 2pp/8pp.

pp/4pp –/– 2pp/2pp = 2pp/8pp

pp/4 • 2pp/2pp = 2pp/8pp

pp • 2pp/4pp • 2pp = 2pp/8pp

2pp/4pp • 2pp = 2pp/8pp

2pp/8pp = 2pp/8pp.

Axiom #2.

2pp/2pp = pp/pp.

Axiom #3.

pp/4pp –/– pp/pp = pp/4pp.

pp/4pp –/– pp/pp= pp/4pp

pp/4pp • pp/1 = pp/4pp

pp• pp/4pp • pp = pp/4pp

pp/4pp • pp = pp/4pp

pp/4pp = pp/4pp.

Axiom #4.

2pp/2pp = pp.

Axiom #5.

pp/pp = pp.

Axiom #6.

pp/pp • pp/4pp does not equal pp/pp• pp/4pp.

Therefore, pp ≠ pp.