11 Suppose F is an infinite field and fge Frj Show that if f

11. Suppose F is an infinite field and f.ge Frj. Show that if f # g then the functions they induce (from F to F) are different

Solution

If the two components (vectors in a field) are not equal, then the induced functions F(x) at x=f can not be equal to F(x) at x=g as the function is dependent on single variable.

So the function that has one to one mapping can not be equal at two different points.