Real numbers are numbers that exist like 1 421 21342135183 
All numbers are real numbers

infinity is not a real number ( \infty ≠ real number

A real number is any element of the set R,which is the union of the set of rational numbers and the set of irrational numbers. in mathematical expressions,unknown or unspecified real numbers are usually represented by lower case italic letters U through z.The set R gives rise to other sets such as the set of complex numbers and the set of complex numbers. The idea of a real number (and what makes it "real") is primarily of interest to theoreticians. Abstract mathematics has potentially far-reaching applications in communications and computer science, especially in data encryption and security.