May 16th, 2017, 12:11 AM  #1 
Senior Member Joined: Nov 2015 From: hyderabad Posts: 148 Thanks: 1  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: 148 Thanks: 1  Quote:
Thanks  
May 18th, 2017, 04:15 AM  #3  
Math Team Joined: Jan 2015 From: Alabama Posts: 2,487 Thanks: 630  Quote:
Quote:
Quote:
Quote:
Quote:
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: 6,778 Thanks: 2195 Math Focus: Mainly analysis and algebra 
I think you are correct.


Tags 
infinite, subset 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Infinite intersections and infinite unions  Azzajazz  Real Analysis  5  March 10th, 2016 09:01 PM 
Denumerability of a subset of a denumerable subset  bschiavo  Real Analysis  9  October 6th, 2015 11:17 AM 
Relation between an infinite product and an infinite sum.  Agno  Number Theory  0  March 8th, 2014 05:25 AM 
Subset of a Function g[a] subset g[b]  redgirl43  Applied Math  1  April 21st, 2013 06:20 AM 
Infinite set contains an infinite number of subsets  durky  Abstract Algebra  1  March 15th, 2012 11:28 AM 