Cardinal and ordinal numbers are sometimes confused because they have two distinct mathematical definitions. The cardinal numbers in the numbering system should not be confused with cardinal numbers in set theory, in which any method of counting sets using a cardinal number gives the same result. Likewise, the ordinal numbers in arithmetic should also not be confused with ordinal numbers in set theory: Such numbers, often called ordinals for short, are the order type of a well ordered set. They are divided into two types: finite and transfinite ordinals. (For more about sets, ordinals, and cardinal numbers, see “Foundations of Mathematics.”)