function: prove f(i,j)=i+(i+j-1)(i+j-2)/2 is a bijection

[rubelpatel]

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.

[nona.m.nona]

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(x₁)= y₁ equals f(x₂) = y₂, then x₁ equals x₂.

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.