Consider a function f:N x N -> N where f(i,j)=i+(i+j-1)(i+j-2)/2. Prove that f is a bijection.
To complete the proof, follow the usual method:
Show that the function is one-to-one by proving that, if f(x
_{1})= y
_{1} equals f(x
_{2}) = y
_{2}, then x
_{1} equals x
_{2}.
Show that the function is onto by proving that, for any y in the image, you can find an x in the pre-image.
If you experience difficulties, kindly please reply with a clear statement of your work and reasoning so far. Thank you.