Contrary
We need the magic of Contrary to create Invariance.
Two things 'contrary' come together to create identity.
In multiplication "half" and "double" multiply together to create identity. For multiplication this is one. Half and double are contrary with respect to multiplication.
In addition +2 and -2 add together to create identity. For addition this is zero. The integers +2 and -2 are contrary with respect to addition.
A rotation of 90 degrees clockwise and a rotation of 90 degrees counterclockwise are contrary.
We can show contrary at work by showing some math that takes 10 inches to 25.4 centimeters. One equals the other because 1 inch = 2.54 centimeters.
10 in
10 (1) in
10 (2.54/1) (1/2.54) in
(2.54/1) 10 (1/2.54) in
25.4 (1/2.54) in
(25.4)(0.3937) in
The math of the above statement is "math legal", we could stop there. However, 0.3937 in is 1 cm so we can continue...
25.4 (1 cm)
25.4 cm
In the realm of Addition, contrary is whatever number is the negative of the number you choose...