injectivity and surjectivity (onto and one-one)
I was going over my assignment to study for the upcoming midterm, and I thought I had a grasp on surjectivity and injectivity...I don't. Can someone tell me where I went wrong in proving these to 'jectives'.
define g:integers -> integers be defined by g(n)=4n-5. is it injective? surjective?
n=m therefor it is injective
sub back into the equation g(a)=4a-5 to get 4[(b+5)/4]-5
=b, so therefor it is surjective
I think this is correct, but he wrote something along the lines of f(x)=2 has no solution in integers. This is true, so why does my way of doing surjectivity not work. What am I doing or assuming wrong?