- #1
cragar
- 2,552
- 3
I thought of a way to use Gaussian integers to show that NxN~N
We look at (1+i)(1-i) and this corresponds to the coordinate (1,1)
then (1+2i)(1-2i)-->(1,2) then (1+3i)(1-3i)-->(1,3)... and you keep doing this, so we have injected NxN into N.
We look at (1+i)(1-i) and this corresponds to the coordinate (1,1)
then (1+2i)(1-2i)-->(1,2) then (1+3i)(1-3i)-->(1,3)... and you keep doing this, so we have injected NxN into N.