Take the set N={1,2,3,...n} where n->infinity
Take the number s and let s = n+1

N = {1,2,3,4}, s = 5
N = {1,2,3,4,5,6,7}, s = 8
N = {1,2,3,4,5,6,7,8,...,53234}, s = 53235
N = {1,2,3,...,infinity}, s = infinity + 1

As you can see, s does not feature in N; therefore N is uncountable.