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.