because I don't have trouble understanding the value of zero/null/undef/nothing, they're all different words representing the same thing, mathematically or otherwise.

"undef" means "undefined" which is quite different from "zero" or "nothing". Perl treats "undef" as zero (or the empty string) but only after emitting a warning. The warning is only required because "undefined" does not mean the same things as "zero", "nothing", nor "empty".

In C, NULL mostly means "zero" but is often used for "missing" which might represent "undefined". In SQL, NULL means "not present" which is close to "undefined". The this built-in confusion on what "null" means could easily spread to confusion on what "undefined" means.

If you called your bank and asked for balance and they said "I don't know; the computer system is down for maintenance and I can't look it up right now", then that would be getting a balance of "undefined" (or "unknown"). This is much different than a balance of "zero". Surely you can see that.

So it appears that you do have a problem understanding a couple of those terms.