(Just to make the facts straight,) did you know that your facts are actually on my side. Let's try those two examples you gave:

if (undef != 0) {#in number context, undef evaluates to 0, and we know
+ "0 != 0" does not stand.
   print "pg is wrong!";
} else {
   print "pg is right!";
}
[download]

and

if (undef ne "") {#string context
   print "pg is wrong!";
} else {
   print "pg is right!";
}
[download]

Both print "pg is right!".

Also when you say undef is "does not exist". That's also wrong.

Look at this piece of code:

my $a;
[download]

The moment I said this, a memory structure, called SV structure is allocated, so $a exists, although it holds undef value.