## Summary

1.                      We discussed forms of data and processes relevant to an electronic till in a supermarket. In particular, we introduced the idea of a sequence of data items.
2.                      A number of fundamental forms of data were introduced. We distinguished two types of number: integers (positive or negative whole numbers, or 0), and real numbers (thought of as decimal numbers and approximated in computers as floating point numbers). Characters may be thought of as symbols that may be entered from a computer keyboard by a single keystroke. Each character is associated with an integer code and we introduced one such encoding called the ASCII code. The Boolean values true and false form another fundamental form of data.
Data may be structured in a collection. Different forms of collection are possible. We looked at two: sets and sequences. In a sequence, the order in which the items appear in the collection is important and an item may appear more than once. In a set, one is only interested in the different items appearing in the collection, and the order in which these items are listed is of no significance, nor is repetition of an item.

# 5 Operations and comparisons

## Seeing processes as functions

Addition of numbers is a process that one would expect a computer to be able to perform. Now we write the result of adding the numbers 5 and 2 as 5 + 2, for example. The symbol +, which represents the process of addition, appears between the two numbers being added. This is known as infix notation. Infix notation may be used for processes that combine two data items of the same type. Addition, subtraction and multiplication of numbers are familiar examples. We also use infix notation when writing a comparison of the size of two numbers, such as 5 < 9.
In this section, we shall show that a process such as addition of numbers is a function. Perhaps more surprisingly, a process such as < can also be seen as a function. This perception is a necessary preliminary to seeing how such a process can be implemented by a computer.