How to prove that there’s always at least one rational number between two real numbers?

1 Answer
Feb 3, 2018

See explanation...

Explanation:

Given two real numbers #a < b#, choose an integer #N > 1/(b-a)#

Then #b-a > 1/N#

If #b# is an integer multiple of #1/N# then #b-1/N# is a rational number in #(a, b)#

Otherwise #floor(bN)/N# is a rational number in #(a, b)#