# How to prove $(\mathbb{R}\backslash \mathbb{Q})\cap (x,y)\neq \emptyset$ for $x,y\in \mathbb{R}$ and $x<y$? [duplicate]

How to prove $$(\mathbb{R}\backslash \mathbb{Q})\cap (x,y)\neq \emptyset$$ for $$x,y\in \mathbb{R}$$ and $$x?

Sorry, but I don't even know how to start. Any ideas and impulses?

## marked as duplicate by José Carlos Santos real-analysis StackExchange.ready(function() { if (StackExchange.options.isMobile) return; $('.dupe-hammer-message-hover:not(.hover-bound)').each(function() { var$hover = $(this).addClass('hover-bound'),$msg = $hover.siblings('.dupe-hammer-message');$hover.hover( function() { $hover.showInfoMessage('', { messageElement:$msg.clone().show(), transient: false, position: { my: 'bottom left', at: 'top center', offsetTop: -7 }, dismissable: false, relativeToBody: true }); }, function() { StackExchange.helpers.removeMessages(); } ); }); }); May 9 at 16:34

Find a nonzero rational $$r$$ such that $$x\sqrt 2