Show that if , and , then there exist -neighborhoods of and of such that =

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- Sep 3rd 2008, 11:20 AMhockey777Real Numbers - Real Anaylsis
Show that if , and , then there exist -neighborhoods of and of such that =

- Sep 3rd 2008, 11:24 AMPlato
Let .

- Sep 3rd 2008, 11:35 AMhockey777
any reason why you divided by 4?

- Sep 3rd 2008, 11:38 AMPlato
- Sep 3rd 2008, 11:40 AMhockey777
Sorry one more question. What else was throwing me off in this problem was the fact I don't think it's clear for a beginner like me. I think the problem suggest that should be the same for both, but I'm not sure. Is that true?

- Sep 3rd 2008, 11:54 AMPlato
No there is no requirement the neighborhoods have the same radius.

But I gave you a value that will work for both.

Let .

Now suppose that .

That is a clear contradiction.

So U & V must have nothing in common.