section_path: Extensions of the concept/Transfinite numbers
section_name: Transfinite numbers
paragraph_text: Transfinite numbers
  
  For dealing with infinite sets, the natural numbers have been generalized to the ordinal numbers and to the cardinal numbers. The former gives the ordering of the set, while the latter gives its size. For finite sets, both ordinal and cardinal numbers are identified with the natural numbers. In the infinite case, many ordinal numbers correspond to the same cardinal number.