BdMO National Higher Secondary 2019/8
 samiul_samin
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 Joined: Sat Dec 09, 2017 1:32 pm
BdMO National Higher Secondary 2019/8
The set of natural numbers $\mathbb{N}$ are partitioned into a finite number of subsets.Prove that there exists a subset of $S$ so that for any natural numbers $n$,there are infinitely many multiples of $n$ in $S$.
 samiul_samin
 Posts: 1007
 Joined: Sat Dec 09, 2017 1:32 pm
Re: BdMO National Higher Secondary 2019/8
Hint
Short Solution
It can also be proved by contradiction as finite×finite not equals to infinite.

 Posts: 21
 Joined: Sat Jan 28, 2017 11:06 pm
Re: BdMO National Higher Secondary 2019/8
May be this answer is not correct as the question asked to prove that there exists a subset $S$ such that in $S$ there are infinitely many multiples of any natural number $n$.
here you have proven for a natural number $n$ there is a subset which have infinite multiple of $n$. But you have to prove in subset $S$ there are infinity many multiples of any natural number $n$
here you have proven for a natural number $n$ there is a subset which have infinite multiple of $n$. But you have to prove in subset $S$ there are infinity many multiples of any natural number $n$