Deleting dynamically allocated variables setting pointer to 0

After array has been returned to the OS, there is no need to assign it a value of 0, right?

You're right it is not needed because the memory is freed (deallocated) by the operator delete. But think of a case where you may use the pointer in another place in your code (functions, loops, etc.) after you use delete[] on it.

The array variable still holds the address of the old allocation after the delete[] statement was called (dangling pointer). If you would access that address you would get undefined bahaviour (UB) because the memory is no longer yours, in most of the cases your program would crash.

To avoid that you do a null pointer check like:

if (array != nullptr)
{
   /* access array */
   ...
}

which is checking the pointer against the address 0 which represents an invalid address.

To make that check possible you set the pointer to nullptr or NULL if C++11 is not available. The nullptr keyword introduces type safety because it acts like a pointer type and should be preferred over the C-like NULL. In pre C++11 NULL is defined as integer 0, since C++11 it's an alias to nullptr.
To define your own nullptr to use it for pre C++11 compiler look here: How to define our own nullptr in c++98?

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An interesting fact about delete or delete[] is that it is safe to use it on a nullptr. It is written at point 2 on cppreference.com or at this SO answer.

operator delete, operator delete[]

2) [...] The behavior of the standard library implementation of this function is undefined unless ptr is a null pointer or is a pointer previously obtained from the standard library implementation of operator new[](size_t) or operator new[](size_t, std::nothrow_t).

We are setting pointers to NULL (0) to avoid dangling pointers (pointer is still pointing to same memory which is no longer yours). In case of local variables it is not that useful if function doesnt continue after delete (so its obvious pointer won't be reused). In case of global/member poitners its good practice to avoid bugs.

Accessing already deleted pointer may lead to overwriting/reading random memory (it might be more dangerous than crash) and causes undefined behavior, while accessing NULL pointer will immediatelly crash.

Since c++11 you should use nullptr because its defined as pointer type while NULL is more int type and improves type safety + resolves ambiguous situations.

In case of double deleting pointer, its safe to use delete on nullptr and nothing happens but if you delete already deleted non-null pointer, it will cause undefined behavior and most likely program will crash.

In c++ you should avoid using pure pointers since there are STL containers (which frees their resources them self (RAII)) for this usage or smart pointers.

std::vector<int> array{1,2,3,4,5};

This is done so that the pointer is set to NULL (whether in C++, we prefer nullptr, since NULL and 0 may be different things).

This tactic eliminates the possibility of a dangling pointer, because the array may have been deleted, but that doesn't mean that it's set to NULL.

If we don't do that, we run the risk of checking whether the pointer is NULL or not (latter in our code), we will see that it's not NULL, wrongly believe that the pointer is OK to be accessed, and cause Undefined Behavior.