Question

proof of the set of natural numbers are infinite

Answer 1

cool !
so wanna follow Archimedes proof ?

Answer 2

use induction .....

Answer 3

Suppose N is the largest natural number so that the set of natural numbers is {0, 0+1, 1+1 , 1+1+1, ..., N-2, N-1, N} . But by the axioms of natural numbers, N+1 is also a natural number, and N+1 is obviously not in this set. Thus N is not the largest natural number, and since N was arbitrary, there is no largest natural number.
Unlike this set, the blades of grass outside your residence, while a very large number, is nothing compared to the (still finite!) set of all grains of sand in the world, much less the infinite set of natural numbers.

Answer 4

i hope u understood :)