 ラッセル関係電子書籍一覧 |
the associative law: (a + b) + c = a + (b + c)
the commutative law: a + b = b + a
with analogous laws for multiplication and
the distributive law a x (b + c) = (a x b) + (a x c)
Beginners in mathematics are always informed of these laws without being given proofs of them, or, if proofs are offered, they use mathematical induction and are therefore only valid for finite numbers. The ordinary definitions of addition and multiplication assume that the number of sumands or factors is finite. This is among the limitations which we set ourselves to remove.
Source: My Philosophical Development, 1959, by Bertrand Russell
More info.: https://russell-j.com/beginner/BR_MPD_08-080.HTM