If I_\n = \{\x \epsilon \R : - 1/\n

TS ICET 23 May 2018 Shift 2 Paper

Question : 113 of 200

Marks: +1, -0

I_\n

\{\x \;ε \;\R : - 1/\n<\x<1/\n\}

for n = 1,2,3,..... then

∩↖{∞}↙{n=1} \I_\n

Solution:

I _{ n }=\{ x ∈ R ; \;{-1}/{ n }< x <\;{1}/{ n }\}

I _{1}=(-1,1) \;\; I _{2}=(\;{-1}/{2}, \;{1}/{2})

I _{3}=(\;{-1}/{3}, \;{1}/{3}) . . . . . .

⋂_{n=1}^{∞}\;\;I _{ n }= I _{1} ∩ I_{2} ∩ I_{3} . . . . . .

=\{0\}

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