Cardinality of is the same as cardinality of (0,1), because there is a bijection from first set to second:
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 and insert them to coordinates respectively. It is a bijection from [0,1] to (0,1].
Then set cut a sequence of points and insert them to coordinates respectively. It is a bijection from (0,1] to (0,1).
Cardinality of is less then cardinality of , because is a countable set and is a continuum. has the same cardinality as .
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