Can you prove that [tex]\mathbf{R}[/tex] and [tex]\mathbf{R}-\mathbf{Q}[/tex] have same cardinality?(adsbygoogle = window.adsbygoogle || []).push({});

One way would be to say that [tex]\mathbf{R}-\mathbf{Q}[/tex] is not countable and must have cardinality <= [tex]\mathbf{R}[/tex] and invoke the Continuum Hypothesis to conclude that its cardinality is aleph-1 same as that of [tex]\mathbf{R}[/tex]..

Somehow this does not look appealing...

Can you explicitly construct a bijection and help me to visualise the situation better??

Thanks.

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# Construction of bijection

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