a) The inclusion Z -> R is a homomorphisms of additive groups.
b) The subgroup {0} of Z is isomorphic to the subgroup {(1)} of S5.
These are both true statements, but I must know how to prove them. Can someone show me please? Thanks.
a) The inclusion Z -> R is a homomorphisms of additive groups.
b) The subgroup {0} of Z is isomorphic to the subgroup {(1)} of S5.
These are both true statements, but I must know how to prove them. Can someone show me please? Thanks.
So I googled it and it looks like the inclusion map of function f is defined by f(x) = x. So to show that f: Z->R is an homomorphism, I must show that f(x+y) = f(x) + f(y). But f(x+y) = x+y and f(x) + f(y) = x+y. So were done. COrrect?