What is 2.7 in the real number system?

Answer 1

The number 2.7 is defined by the Dedekind cut.

The Dedekind cut for any real number divides the set of rational numbers, Q, into two disjoint sets: set A which consists of all number less than the given number (2.7) and set B, which is the complement of A in Q. If the set B has a minimum then that number is the minimum of set B. If not then the number is the real number that is not in A nor in B.

For all rational numbers B has a minimum. So in this case, the number is the Dedekind cut defined by the set B = {x | x in Q, x not < 2.7}