The operations of addition and multiplication of two given cardinal numbers can be defined by taking two classes a and 13, satisfying the conditions (1) that their cardinal numbers are respectively the given numbers, and (2) that they contain no member in common, and then by defining by reference to a and (3 two other suitable classes whose cardinal numbers are defined to be respectively the required sum and product of the cardinal numbers in question.
Thus, corresponding to the cardinal numbers 2, 3, 4.
Also in addition to the cardinal numbers there are the ordinal numbers: the fifth apple and the tenth pear claim thought.
A critical defence of them would require a volume.1 Cardinal Numbers.
If s is any class and zero is a member of it, also if when x is a cardinal number and a member of s, also x-}-I is a member of s, then the whole class of cardinal numbers is contained in s.