arraysiterationinvariants data is ultimately stored in computers as patterns of bitsthough these days most programming languages deal with higher level objectssuch as charactersintegersand floating point numbers generallywe need to build algorithms that manipulate collections of such objectsso we need procedures for storing and sequentially processing them arrays in computer sciencethe obvious way to store an ordered collection of items is as an array array items are typically stored in sequence of computer memory locationsbut to discuss themwe need convenient way to write them down on paper we can just write the items in orderseparated by commas and enclosed by square brackets thus[ is an example of an array of integers if we call this array awe can write it asa [ this array has itemsand hence we say that its size is in everyday lifewe usually start counting from when we work with arrays in computer sciencehoweverwe more often (though not alwaysstart from thusfor our array aits positions are the element in the th position is and we use the notation [ to denote this element more generallyfor any integer denoting positionwe write [ito denote the element in the ith position this position is called an index (and the plural is indicesthenin the above examplea[ [ [ and so on it is worth noting at this point that the symbol is quite overloaded in mathematicsit stands for equality in most modern programming languagesdenotes assignmentwhile equality is expressed by =we will typically use in its mathematical meaningunless it is written as part of code or pseudocode we say that the individual items [iin the array are accessed using their index iand one can move sequentially through the array by incrementing or decrementing that indexor jump straight to particular item given its index value algorithms that process data stored as arrays will typically need to visit systematically all the items in the arrayand apply appropriate operations on them