Define f: ℕ×ℕ→ℕ as follows: For each (m,n) ∈ ℕ×ℕ,

Prove that f is an injection.

I don't know how to go about doing this one.

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- Apr 23rd 2010, 04:52 PMdwsmith[SOLVED] Relations
Define f: ℕ×ℕ→ℕ as follows: For each (m,n) ∈ ℕ×ℕ,

Prove that f is an injection.

I don't know how to go about doing this one. - Apr 23rd 2010, 06:52 PMDrexel28
- Apr 23rd 2010, 07:03 PMdwsmith
- Apr 23rd 2010, 07:04 PMDrexel28
- Apr 23rd 2010, 07:05 PMdwsmith
- Apr 23rd 2010, 07:07 PMDrexel28
- Apr 23rd 2010, 07:08 PMdwsmith
- Apr 23rd 2010, 07:09 PMDrexel28
- Apr 23rd 2010, 07:10 PMdwsmith
The left is even and the right is odd.

- Apr 23rd 2010, 07:12 PMDrexel28
- Apr 23rd 2010, 07:14 PMdwsmith
- Apr 23rd 2010, 07:16 PMDrexel28
- Apr 23rd 2010, 07:20 PMdwsmith
- Apr 23rd 2010, 07:21 PMDrexel28
[QUOTE=dwsmith;499960]Well if it equals zero, the left is odd and the right is odd. [quote]

Which is good!

Quote:

If it is >0, the right is even and the left is odd.

So...it must be true that?! - Apr 23rd 2010, 07:24 PMdwsmith
[quote=Drexel28;499961][quote=dwsmith;499960]Well if it equals zero, the left is odd and the right is odd.

Quote:

Which is good!

Which is bad!

So...it must be true that?!