Prove :
if a and b are any positive integers, then there exists a positive integer n such that n*a = b

Question

Prove :
if a and b are any positive integers, then there exists a positive integer n such that n*a >= b

ikram002p · Answer

assume the statment is not true, so for some a,b 
na>b for positive integer n then the set 
S={b-na , n positive integer}
by the "well-ordering princple" S will posses a least element  ,say b-ma.
notice that b-(m+1)a  also lies in S.
becouse S contains all integer of the form , furthermore, we have
b-(m+1)a=(b-ma)-a<b-ma
contrary to the choice of b-ma as the smallest integer in S . this contradiction arose out of our original assumption that the Archimeadean property didnt hold; ence this property is proven true.
got it or still confused ??

ikram002p · Answer

actually this one :P
i have doubt if u got it xD
@ganeshie8