How are they different?
Find inf, sup of S
1) S= {1/n | n in N}
2) S ={1/n | n in Z, n 0}
3) S ={1/n | n in Z , n = 0}
Please, help

Question

How are they different?
Find inf, sup of S
1) S= {1/n | n in N}
2) S ={1/n | n in Z, n >0}
3) S ={1/n | n in Z , n> = 0} 
Please, help

mathmath333 · Answer

sry 1.) inf =0,sup=1 ???

mathmath333 · Answer

inf means lowest?

mathmath333 · Answer

and vice versa

loser66 · Answer

inf means the greatest lower bound

mathmath333 · Answer

so m i correct

loser66 · Answer

Yes, but put it in logic, please

mathmath333 · Answer

i never heard of this questions

mathmath333 · Answer

well S will be maximum only at n=1

loser66 · Answer

Like: 
Claim inf S = 0, 
Proof: $\forall n \in N$ $\dfrac{1}{n}<0 $

mathmath333 · Answer

and s will be lowest on 1/infinty =0

loser66 · Answer

but sup S is not 1, I think

loser66 · Answer

if I take n = 0.5 , n is in N, and 1/n = 2 > 1, so that 1 can't be upper bound of S

mathmath333 · Answer

nut u specified n is in set of natural numbers and 0.5 is not natural number

loser66 · Answer

oh yes, I just realize that, I am sorry, my bad

mathmath333 · Answer

i mean but u specified ,lol

loser66 · Answer

Ok, 
next n in Z

loser66 · Answer

The same, right?

loser66 · Answer

for the third case, $n\in Z, n\geq 0$ is the same, still. right?

mathmath333 · Answer

yes 1 and 2 are same

mathmath333 · Answer

no

mathmath333 · Answer

i think its inf=1 and sup =1/0=infinity

mathmath333 · Answer

not sure lol

loser66 · Answer

Ok, thank you so much. I got what happen.

mathmath333 · Answer

mathmath333 · Answer

hey wait

mathmath333 · Answer

for third it will be inf =1/infinity=0 and sup=1/0=infinity

mathmath333 · Answer

tricky

loser66 · Answer

when n goes to 0 , 1/n either goes to $\infty$ or $-\infty$
so that sup, inf don't exists.

loser66 · Answer

but if we break it down to 2 intervals $[-\infty, 0]$ and $[0,\infty]$ then we have inf for each = 0

mathmath333 · Answer

for third question but n>=0 so it will be positive infinity right?

loser66 · Answer

yes,

mathmath333 · Answer

so it means infium exists for question 3 as zero

loser66 · Answer

yes,

loser66 · Answer

hey, I am the Asker, not you. hehehe... You are helping me. How can it turn to I answer your question situation?? hahahha

mathmath333 · Answer

lol its typical way of answering/interacting...dont like  other boring ways

loser66 · Answer

Anyway!!! thanks for your help.

mathmath333 · Answer

welcome your