Normally we'd say "a null pointer" because there can be many pointers with this value. Of course the value itself is unique, so we can say "... with the null value", but as the value fields are plural, we can say "... with a null value field" or "... with a null value". These would be common describing the programming language C or the basic machine operations. If you're speaking abstractly, you might well say "the biggest problem for debugging is the null pointer", exactly as we speak of "the whale" to mean the species.
It's easiest to understand by comparing with a conventional numeric variable. "Zero-valued variables" is plural, hence "a zero-valued variable", and "a variable with the value zero". But it's also perfectly correct idiomatically to write "all the variables with zeroes in them".
Essentially it's about whether you are thinking of the many places of these pointer variables, or some single distinguished value.
In programming languages where the uniqueness of a given object is important, such as Python, often you don't speak of pointers, and would very frequently write "the null object, the true object", etc.
To comment on your example, it reads as if it is confused between a pointer and a pointer to a pointer. (In C programming terms a
char * vs
Set the pointer to a/the null pointer.
This would normally be something like one of these:
- Set the pointer to null
- Make p a null pointer