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Which of the following sets have the same cardinality? Select all that apply. LaTeX: \mathbb{N} N [0,1] LaTeX: \mathbb{R} R (0,1)

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Cardinality of \mathbb{R} is the same as cardinality of (0,1), because there is a bijection from first set to second: \dfrac{1}{1+e^{-x}}


Cardinality of [0,1] is the same as cardinality of (0,1), because there is a bijection from first set to second:

From the first set cut a sequence of points 0,1/4, 1/4^2, 1/4^3, \dots and insert them to coordinates 1/4, 1/4^2, 1/4^3, 1/4^4, \dots respectively. It is a bijection from [0,1] to (0,1].

Then set cut a sequence of points 1,(1-1/4), (1-1/4^2), (1-1/4^3), \dots and insert them to coordinates (1-1/4), (1-1/4^2), (1-1/4^3), (1-1/4^4) \dots respectively. It is a bijection from (0,1] to (0,1).


Cardinality of \mathbb{N} is less then cardinality of \mathbb{R}, because \mathbb{N} is a countable set and \mathbb{R} is a continuum. \mathbb{R} has the same cardinality as 2^\mathbb{N}.


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Question ID: mtid-5-stid-8-sqid-3860-qpid-2559