Is there a bijection between $\mathbb{Z}\times\mathbb{Z}\times\dots$ for countably infinitely many $\mathbb{Z}$'s and $\mathbb{R}$? That is, is $\mathbb{Z}\times\mathbb{Z}\times\dots$, repeated countably infinitely many times, uncountable?
Bijection between $\mathbb{Z}\times\mathbb{Z}\times\dots$ and $\mathbb{R}$
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elementary-set-theory
cardinals
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2The question after "that is" is not equivalent to the question in the first sentence; not all uncountable sets have the cardinality of $\mathbb R$. – 2012-12-06
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1What other sets do you know to be uncountable? What other sets do you know to be "bijectable" with $\mathbb{R}$? – 2012-12-06