Each element of an array is accessed and indexed by a number known as a(n) _________.

In computer science, an array is a fundamental data structure used to store a collection of elements that are usually of the same data type. Arrays are useful for storing data that is naturally ordered or needs to be easily manipulated as a group, like numbers in a list, characters in a string, or even other arrays.

Consider an array as a row of mailboxes in an apartment building, each holding a piece of data. These mailboxes are arranged consecutively, and to identify each one, we use a unique number called an 'index'. In programming, arrays are generally created with a predefined size, which tells you how many 'mailboxes' or elements the array can house.

For example, in the programming language Python, you might see an array declared as arr = [10, 20, 30, 40]. This 'arr' array contains four integer elements. It is important to know how to properly access and manipulate these elements, which ties into the concepts of zero-based indexing and array access, which we shall explore further.

Zero-based indexing is the standard method for array indexing in many programming languages, where the index of the first element is 0. Think of it as the ground floor of a building being labeled as floor 0 instead of 1 — it's simply a starting point.

Under zero-based indexing, the second element is accessed with the index 1, the third with 2, and so on until the last element, which is accessed with an index of 'length of the array - 1'. This might seem counterintuitive at first, but it has practical reasons behind it, such as simplifying the mathematics when calculating the memory address of each element.

For instance, in the earlier array arr = [10, 20, 30, 40], to access the first element '10', we would use the index 0 as in arr[0]. Understanding this concept is crucial because it prevents errors when trying to access array elements and is a foundational aspect of efficient programming.

Array access refers to the retrieval or modification of an element within an array using its index. It's like retrieving mail from a specific mailbox using its unique number. In programming, this is done using square brackets surrounding the index.

For example, if we want to access the third element in our array arr = [10, 20, 30, 40], we would write arr[2] because, in zero-based indexing, the third element is at index 2. Similarly, if we wanted to change the value of the second element from 20 to 25, we would assign a new value by writing arr[1] = 25.

Remember, trying to access an index that is outside the bounds of the array, such as arr[4] in an array with only four elements, would result in an 'index out of range' error. Carefully handling array access is essential for error-free coding and efficient manipulation of data within programs.