I proved that [0,1) has the same cardinality as (0,1], by defining a function and then checking injectivity/surjectivity. I proved [0,1] has the same cardinality as (0,1), by defining a function and showing it has an inverse. I now have to prove that (0,1] has the same cardinality as [0,1], and I can use any of the equivalences established above. What method should I use to do this? Edit: I know how to prove it using previous methods (defining a function and proving bijection), I just want to know if this can be done another way- using equivalence relations maybe?