- #1
member 587159
Hello all. I have a question about a reflexive relation.
Consider ##1_V : V \rightarrow V## with ##V## a vector space. Obviously, this is an isomorphism. My book uses this example to show that V is isomorphic with V (reflexive relationship). However, suppose I have a function ##f: V\rightarrow V## and this function is not ##1_V## but the function is an isomorphism too. Does that prove the reflexivity too? I do understand that using the identityis the easiest way, though.
Thanks in advance.
Consider ##1_V : V \rightarrow V## with ##V## a vector space. Obviously, this is an isomorphism. My book uses this example to show that V is isomorphic with V (reflexive relationship). However, suppose I have a function ##f: V\rightarrow V## and this function is not ##1_V## but the function is an isomorphism too. Does that prove the reflexivity too? I do understand that using the identityis the easiest way, though.
Thanks in advance.