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Write a proof that proves the Union Un an element of natural numbers (-1/n, 2-1/n)=(-1, 2).Also write a proof that proves the intersectionn an element of natural numbers (-1/n, 2-1/n)=[0,1].

Question

Write a proof that proves the Union Un an element of natural numbers (-1/n, 2-1/n)=(-1, 2).

Also write a proof that proves the intersectionn an element of natural numbers (-1/n, 2-1/n)=[0,1].

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Step 1

The given interval is (-1/n,2-1/n) where natural number n belongs to positive integers. So that we assume that the interval I is:

I = }
,2
п
п
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I = } ,2 п п

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Step 2

Put n=1, n=2, n=3, n=4…… then,

 

(11)
1 7
4 4
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(11) 1 7 4 4

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Step 3

At n→∞ {-1/n} is never zero it gets closed to zero and similarl...

I,m2 (0,2)
n,no
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I,m2 (0,2) n,no

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