Advanced Mathematics

Introduction 

Consider a scientist doing an experiment; he/she is collecting data every day. Let 1 u be the data collected the first day, 2 u be the data collected the second day,  be the data collected the third day, and so on…, and n u be the data collected after n days. Clearly, we are generating a set of numbers with a very special characteristic. There is an order in the numbers; that is, we actually have the first number, the second number and so on. A sequence is a set of real numbers with a natural order.