advanced linear algebra Let X be a set and F a field Write C

(advanced linear algebra)

Let X be a set and F a field. Write C(X, F) to be the set of functions from X to F Construct an injective function from X into C(X, F)* (the dual of C(X, F)).

Solution

Injective Function:
An injective function or injection or one to one function is a function that preserves distinctness:it never mapsdistinct elements of it sdomain to the sam element of its domain to the sma edomain.the term one-to- one function must not be confused with one-to-one correspondence , whicj uniquely maps all elements in both domain and codomain to eachother

Occasionally, an injective function from X to Y is denoted :F :X Y, using an arrow with a barbed tail The set of injective functions from XTo Y may be denoted  using a notation derived from that used for falling factorial powers, since if X and Y are finite sets with respectively m and n elements, the number of injections from X to Y .