And of course, we can have only finitely many places for numbers stored in computers. The number 1 and the number are, technically, different, the former being an integer or whole number and the latter being a real number, although we do not usually bother too much about the distinction. There is a good reason for my stipulating that they will be written as columns, although it has to be faced that any other convention would be possible. What the good reason is will appear later when we get to matrices. I shall use the word point to refer to any real number, rational number, or element of .
Computer scientists use terms like array for elements of , and the word vector is also used.
The difference is that you can usually have anything in an array, while vectors have to have numbers in them, and all the same sort of number. Every real number corresponds to a point on this line, where a point is a very tiny dot. Actually, it is as imaginary as a thing can get. Similarly, by putting another line in through the point at 0 vertically, and putting similar numbers along this line, I have that every point on the graph paper has two numbers specifying its position, traditionally called x and y . This means that I can think of as being like a sheet of graph paper that goes on forever.