Topic

Sequences are to calculus what at calculator is to a scientist. There are many ways to introduce sequences. Here we will follow a somewhat unorthodox way. Indeed, consider a scientist doing an experiment; he is collecting data, let us say, every day. So, put  to be the data collected the first day,  be the data collected the second day, and so on.... and  is the data collected after n days. Clearly, we are generating a set of numbers with a very special characteristic: there is an order on the number, that is, we naturally have the first number, the second number, and so on.... A sequence is by definition a set of real numbers with this natural order. We wil use the notation