Asymmetry in the Real Number Line and: A Proof that \pi + e is an Irrational Number

The set of all Real numbers, R, consists of all Rational numbers, Q, being any ratio of two Integer numbers that does not divide by 0. All other Real numbers that are not a Rational number are contained in the set of Irrational numbers, R/Q. These two subsets comprising all of the Real numbers are known to have distinct cardinalities of differing magnitudes of infinity[2]. When a consecutive ordering of all Rational numbers is established, whereby any unique Rational number can be shown to be disconnected from all other Rational numbers[3], a theorem regarding asymmetry on the Real number line is established. This theorem simplifies the necessary requirements to prove that the summation of two known Irrational numbers is Rational or Irrational.