Because you can't describe any system with just 1 number. You are arbitrarily choosing to only pay attention to the cardinality of a set. If you are discussing

Because you can't describe any system with just 1 number. You are arbitrarily choosing to only pay attention to the cardinality of a set. If you are discussing a vector space, there is more structure than that. This is what the study of linear algebra is all about. The amount of structure you require depends on the question you are asking. Not all questions equate to finding the size of a set. You are like a blind man feeling the tail of an elephant and claiming the elephant's nature is the same as a rope!