Can you define adding 1 to be: f(x) = x + 1 and then define subtracting 1 as the inverse function, f^-1(x) ? (Provided you proceed to define addition inductively)

- Apr 27th 2011, 10:19 PMlamp23Can subtraction be defined as the inverse function of addition?
Can you define adding 1 to be: f(x) = x + 1 and then define subtracting 1 as the inverse function, f^-1(x) ? (Provided you proceed to define addition inductively)

- Apr 27th 2011, 10:47 PMabhishekkgp
well since f(x)=x+1 so x=y-1. moreover 'f' is bijective from R to R. so guess you are right.

- Apr 27th 2011, 10:57 PMlamp23
So I guess it could be defined that way but I don't see any advantage over other definitions.

- Apr 27th 2011, 11:09 PMabhishekkgp
- Apr 27th 2011, 11:25 PMlamp23
Actually some books do talk about x+1 as being the "sucessor function" so maybe it's helpful to think of the operations as functions instead of separate ideas