Den stora tråden om Bitcoin Lightning

We know that a necessary condition for a
function to be called linear is that the following property holds:

f(x+y)=f(x)+f(y)

however if we look at our setting we see that:

f(x+y) = r(x+y) + b

and

f(x)+f(y) = rx+b + ry+b = r(x+y) + 2b

equality (and thus linearity) only holds if

r(x+y)+b = r(x+y) + 2b <==> b = 2b

the later is true if and only if `b=0`. In other words: **Our current fee
function is only linear if we set the base fee to zero.**