Wednesday 12 March 2014

discrete mathematics - Comparing the cardinality of (0,1) and (0,1]

Question
Consider the intervals of real numbers (0,1) = {x | 0 < x < 1} and (0,1] = {x | 0 < x ≤ 1}.



Show that |(0,1)| = |(0,1]|



Work
I stated that since both intervals are uncountably infinite then they have the same cardinality, but this was marked as wrong. How do I actually prove this?

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