Do $\{0, 1\}×N$ and $N×\{0, 1\}$ have the same order type?
Hint: Recall the notion of a successor/predecessor
I am saying they do not and trying to use contradiction.
I have tried to do this by contradiction and assumed that there was a bijective corresponding between them, but I am not too sure on where to go with this, or if there is a different way.
Thank you