Do All Uncountable Sets Have The Same Cardinality?

Do All Uncountable Sets Have The Same Cardinality? Do all uncountable sets have the same cardinality? An uncountable set can have any length from zero to infinite! For example, the Cantor set has length zero while the interval [0,1] has length 1. These sets are both uncountable (in fact, they have the same cardinality, which