Question

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

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

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:

Step 2

Put n=1, n=2, n=3, n=4…… then,

Step 3

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

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