May 16th, 2017, 12:11 AM  #1 
Senior Member Joined: Nov 2015 From: hyderabad Posts: 230 Thanks: 2  Infinite Subset
A subset $S$ of $N$ is infinite if and only if A) $S$ is not bounded below. B) $S$ is not bounded above. C) $\displaystyle \ni $ $n_0$ $\displaystyle \epsilon $ $N$ such that $\displaystyle \forall $ $n$ $\displaystyle \geq $ $n_0$ , $n$ $\displaystyle \epsilon $ $S$. D) $\displaystyle \forall $ $a$ $\displaystyle \epsilon $ $S$, $\displaystyle \ni $ $x$ $\displaystyle \epsilon $ $N$ such that $x < a$. As $N$ is an infinite set which is not bounded above, I'm thinking as it's subset should also possess the same property to be an Infinite set. Correct me If I'm wrong 
May 17th, 2017, 10:21 PM  #2  
Senior Member Joined: Nov 2015 From: hyderabad Posts: 230 Thanks: 2  Quote:
Thanks  
May 18th, 2017, 04:15 AM  #3  
Math Team Joined: Jan 2015 From: Alabama Posts: 3,104 Thanks: 850  Quote:
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Last edited by Country Boy; May 18th, 2017 at 04:18 AM.  
May 18th, 2017, 04:29 AM  #4 
Math Team Joined: Dec 2013 From: Colombia Posts: 7,274 Thanks: 2435 Math Focus: Mainly analysis and algebra 
I think you are correct.


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