送交者: steven 于 2005-6-20, 13:31:28:
回答: if you know what is axiom 由 xinku 于 2005-6-20, 07:59:16:
the formalization of number system. However, without formalization, you won't be able to do "10^100 + 1" since by counting method, there aren't enough atom in the universe to write down the number. Without formalization, the number system won't be very useful since it only deal with things you cannot see. Just like you can plot a time-distance graph of an accelerating object, but without applying Newtonian machanics, you won't be able to predict the time-distance graph of another object.
Arithemic axioms are called Peano Axioms, in which, the axiom of infinity gives the well defined inductive set, start from 0, to any interger. Where addtion is an result of this axiom, which guarantees a consistant behavior under logical operations and that gives you the ability to prove or pridict things in mathematics.