101 is chosen arbitrarily from the numbers 1,2,3,...,199,200. Prove that two of these selected numbers can be found such that one is divisible by the other.
Question. (math analysis)
(X ,d ) is a metric space and
(p_n )_(n=1) ^∞ is a sequence in X.
(p_n )_(n=1) ^( ∞) is cauchy if and only if
lim_(N→∞) diam (E_N )=0.
where , E_N = { p_N , p_(N+1) , ...}
diam E:=sup{d(x,y)∣x,y ∈E }