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I know that 2 countable infinities are considered equal because you can pair each element in one set two an element in another one. But, for example, if we let all real numbers between 3 and 5 be equal to A, and all real numbers between 2 and 6 be equal to B, do we consider

B = A or B > A ?

I wasn't able to find the answer to this question anywhere, I'd really appreciate your help.

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$B \cong A$. You can see this by writing down an explicit bijection $f : B \rightarrow A$. – goblin Jan 30 '14 at 10:38
up vote 4 down vote accepted

The function $x\mapsto2x-4$ is a bijection between $[3,5]$ and $[2,6]$ hence these sets are equipotent (loosely speaking, they have the same size).

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Thanks, that's actually pretty helpful example. I can't believe I was wrong... Bests, SmallCompetitor – BalacaBoyCompetition Jan 30 '14 at 10:42

B = A, because there exists a bijection between [3,5] and [2,6], hence there are the same amount of real numbers is both intervals.

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