let f:NxN->N be defined by f(x,y)=(1/2)(x+y)(x+y-1)-(1-y)
Is f one-to-one? Does f map (NxN) to N or onto N (meaning are all values in N in the range of f or is the range a subset of N)?
Can I get a hint on how to go about answering either of those questions. I know what each of the questions mean, but I have no idea how to answer them.
I think since f:NxN -> N, (-1,1) is not in the domain, so it might still be one-to-one
I set f(x,y)=f(x',y') and couldn't show that it implies (x,y)=(x',y')
how can i tell that there aren't different pairs such that both of these are equal
I am still working on this