Infimum and Supremum of Union and Intersection sequences

[Idealistic]

Let A = U[sub:2tptown5](from n=1 to infinity)[/sub:2tptown5]{-(1/n), 1 + 1/n} and B = (Upside down "U")[sub:2tptown5](n=1 to infinity)[/sub:2tptown5]{-(1/n), 1 + 1/n}

find infA, supA, infB, supB

So I have infA = -1, supA = 2, but I'm confused for B because from n = 1 to infinity, -(1/n) and (1 + 1/n) share no common values so would it just be the supremum and infimum of an empty set for be?

.

 

[pka]

Let A = U[sub:zrwbdy4y](from n=1 to infinity)[/sub:zrwbdy4y]{-(1/n), 1 + 1/n} and B = (Upside down "U")[sub:zrwbdy4y](n=1 to infinity)[/sub:zrwbdy4y]{-(1/n), 1 + 1/n}
find infA, supA, infB, supB
So I have infA = -1, supA = 2, but I'm confused for B because from n = 1 to infinity, -(1/n) and (1 + 1/n) share no common values so would it just be the supremum and infimum of an empty set for be?.

Frankly your notation is hard to read.
\(\displaystyle B = \bigcap\limits_{n = 1}^\infty {\left\{ {\frac{{ - 1}}{n},1 + \frac{1}{n}} \right\}} = \emptyset \,\text{ but } \,B = \bigcap\limits_{n = 1}^\infty {\left( {\frac{{ - 1}}{n},1 + \frac{1}{n}} \right)} = \left( {0,1} \right)\).

Which do you mean?

 

[Idealistic]

\(\displaystyle B = \bigcap\limits_{n = 1}^\infty {\left\{ {\frac{{ - 1}}{n},1 + \frac{1}{n}} \right\}}\)

and A is exactly the same thing except the "union of" (or) instead of the intersection (and).

Am I correct in stating that the infA = -1, and the supA = 2? I'm not sure what infB or the supB are however.

Please help.

 

[pka]

\(\displaystyle B = \bigcap\limits_{n = 1}^\infty {\left\{ {\frac{{ - 1}}{n},1 + \frac{1}{n}} \right\}}\)
and A is exactly the same thing except the "union of" (or) instead of the intersection (and).
Am I correct in stating that the infA = -1, and the supA = 2? I'm not sure what infB or the supB are however.

Well then, the empty set has neither a greatest lower bound nor a least upperbound.