This set includes the golden ratio in addition to all transcendental numbers, such as pi and e. Name this type of real number whose decimal representation neither terminates nor repeats.
A measure of how well numbers in this set can be represented by numbers not in this set is the LiouvilleÂ–Roth constant. One proof showing that a number belongs to this set is based on the fact that two raised to a natural number cannot equal three raised to a natural number, and another is based on the fact that a positive integer cannot be less than the reciprocal of another positive integer. This set includes the golden ratio in addition to all transcendental numbers, such as pi and e. Name this type of real number whose decimal representation neither terminates nor repeats.
A measure of how well numbers in this set can be represented by numbers not in this set is the LiouvilleÂ–Roth constant.
irrationals [or irrational numbers]