MathDB

a) Prove that in an infinite sequence

{a_k}

of integers, pairwise distinct and each member greater than

1

, one can find

100

members for which

a_k > k

.
b) Prove that in an infinite sequence

{a_k}

of integers, pairwise distinct and each member greater than

1

there are infinitely many such numbers

a_k

such that

a_k > k

.
(A Andjans, Riga)
PS. (a) for juniors (b) for seniors

(017) 3