Why can't $m$ or $n$ be zero on $TM_{mn}$ mode in a rectangular waveguide?

The question is: Is there any analytical or practical issue if $$m$$ or $$n$$ becomes zero in $$TM_{mn}$$ mode for a rectangular waveguide? It could probably be a simple question but I'm not sure about why does it happen that those values can't be zero or what is the physical meaning of this and what info does Maxwell's equations give to ensure it can't be $$0$$.

If $m=0$ or $n=0$, the field is zero everywhere in the waveguide (http://web.mit.edu/6.013_book/www/chapter13/13.4.html)