# Bijection

• February 21st 2006, 09:10 AM
juef
Bijection
Hey all,

I know there's a bijection between $\mathbb{R}$ and $\rbrack0,1\lbrack$, but I was wondering if there was one between $\mathbb{R}$\ $\mathbb{Q}$ and $\mathbb{R}$\ $\mathbb{Q}\bigcap$ $\rbrack0,1\lbrack$.

Can anyone help me? Thank you!
• February 21st 2006, 02:51 PM
ThePerfectHacker
What do you mean by $\mathbb{R}/\mathbb{Q}$ because that is used to represent a factor ring but the problem is that $\mathbb{Q}$ is not an indeal in $\mathbb{R}$. Thus you mean something else by the symbol $/$ but I do not know what you mean.
• February 21st 2006, 03:29 PM
juef
Sorry for the confusion, the backslash would mean, in this case, $\mathbb{R}$ without $\mathbb{Q}$, or in other words the irrationals. Indeed, I am not trying to represent a factor ring. :)
• February 22nd 2006, 02:42 PM
ThePerfectHacker
Quote:

Originally Posted by juef
Sorry for the confusion, the backslash would mean, in this case, $\mathbb{R}$ without $\mathbb{Q}$, or in other words the irrationals. Indeed, I am not trying to represent a factor ring. :)

But the cardinality of the irrationals must be the countinuum. Because the cardinality of the rationals is $\aleph_0$.