# Are there more real numbers than irrational numbers? [duplicate]

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Wrapping my head around the mathematical definition of infinity and just curious here: Are there more real numbers than irrational numbers? It would intuitively seem so, but they are both just uncountable infinite sets, right? Some I guess there would be the same number of irrational numbers as real numbers? But I can't imagine a "bijection" between them. (A term I just learned about five minutes ago...)

## marked as duplicate by José Carlos Santos, Dietrich Burde number-theory 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(); } ); }); }); Nov 12 '18 at 19:03

• I'm not sure this is a duplicate. It seems to be asking for an example of a bijection between $\mathbb R \setminus\mathbb Q$ and $\mathbb R$, not why $|\mathbb R\setminus\mathbb Q| > |\mathbb Q|$ – eyeballfrog Nov 12 '18 at 19:09
• Here is an answer that gives a bijection between $\mathbb R \setminus \mathbb Q$ and $\mathbb R$. – Daniel Mroz Nov 12 '18 at 19:13