Prove the set A02U56 has a cardinal number cSolutionCardinal

Prove the set A=(0,2)U[5,6) has a cardinal number c.

Solution

Cardinality of a closed set and an open set are equal . Let the cardinality for Real numbers be c/2 . We can make a one-one mapping from (0,2) -> R resulting in the same cardinality . SInce [5,6) will have same cardinality as (5,6) and similar mappings to Real Numbers , hence cardinality for the given set would be c/2 + c/2 = c