1. Concept:
- Monochromatic: An object has only one image, Never two.
- Fully: All elements of an image have a preimage
- Dual luster: Both single luster and full luster (Song = 2 => both of them)
2. Exercise
Prove that the following mapping is bidirectional f(x)= 2x+3, x∈R
CM Monotone:
Let x1, x2 be any of R and x1≠x2
I have:
- f(x1) = 2(x1)+3
- f(x2)= 2(x2)+3
Since x1≠x2, f(x1)≠f(x2)
Conclusion: f monochromatic (1)
CM Full of light:
Let’s take any y in R. We have: 2x+3=y => x=(y-3)/2
We can always find x when y or f(x) is defined for all y.
Conclusion f is all-inclusive (2)
So from (1) and (2) f are parallel
