 A cardinal number (like “one”, “two”, “three”)—also called a cardinality—represents how many elements a set has. Two sets have the same cardinal number if it is possible to come up with any correspondence at all between the members of one and the members of the other, even if this correspondence fails to respect the ordering or any other structure of the sets. Two finite sets have the same cardinal number if and only if they have the same ordinal number. For infinite sets, if they are well-ordered and have the same ordinal number, then they have the same cardinal number (because two sets well-ordered with the same order type have a unique correspondence between elements in corresponding positions of the ordering). But they may have the same cardinal number without having the same ordinal number: we have seen that sets of one cardinality can be represented with many different order types.