the answer is yes, but i need to show an example, would i just do it like pi+ square root 2 or would i need to do a proof by contradiciton, could i please have a worked solution please.
also if n is any positive integer then sqrt(2)/n is irrational. notice that this means we can find irrational numbers as small as we like simply by increasing n.
use the fact that sqrt(2)/n can be made as small as we desire to show that between every pair of distinct rational numbers there is an irrational number. that is suppose x Є Q and y Є Q and that x < y show that there is an irrational number z with x < z < y