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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.

- rubelpatel
**Posts:**1**Joined:**Wed Aug 03, 2011 6:49 am

rubelpatel wrote: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

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.

- nona.m.nona
**Posts:**260**Joined:**Sun Dec 14, 2008 11:07 pm

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