08/22/2012, 10:20 PM
if x^3 = 1 and x=/= 1
then x^4 = x
this implies that x^2 =/= x and also that x^2 =/= 1
hence let y =/= x and =/= 1
x^2 = y
y^2 = needs to be x since y^2 = x^4.
x^2 = y
y^2 = x
x*y = 1
follows
another way to arrive at the multiplication table.
more my style i guess but perhaps harder to follow.
seems i wanted to share it.
regards
tommy1729
then x^4 = x
this implies that x^2 =/= x and also that x^2 =/= 1
hence let y =/= x and =/= 1
x^2 = y
y^2 = needs to be x since y^2 = x^4.
x^2 = y
y^2 = x
x*y = 1
follows
another way to arrive at the multiplication table.
more my style i guess but perhaps harder to follow.
seems i wanted to share it.
regards
tommy1729