On simple continued fractions

This thesis presents a study concerning a sequence of real numbers which gives rise to a continued fraction whenever the second equation is substituted to the first equation and each fraction after the second is substituted to the denominator of the fraction which precedes it in the sequence.Simple continued fractions are governed by certain theorems, that cover rational numbers expressible as simple finite continued fractions and vice versa, and irrational numbers expressible as simple infinite continued fractions and vice versa. These theorems are organized, analyzed, proven and completed. In addition, examples are provided for better understanding of such theorems