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**Dragonshade****Member**- Registered: 2008-01-16
- Posts: 147

Got some problems with my textbook's wording

What does it mean by "For all but finitely many"? is there an equivalent way to word it?

What does it mean by adjoined? Rudin didn't explain this term in his book

Thanks in advance : )

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**LQ****Real Member**- Registered: 2006-12-04
- Posts: 1,285

a sequence p + p(1) + .... + p(n) ∈ X if and only if p(n) < p(n-1) for n = ∞.

PS. hit up sequence at wikipedia.

*Last edited by LQ (2010-06-25 00:45:05)*

I see clearly now, the universe have the black dots, Thus I am on my way of inventing this remedy...

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**Ricky****Moderator**- Registered: 2005-12-04
- Posts: 3,791

Dragonshade:

1. The standard analysis way to word this is:

A sequence {p_n} converges to p in X if and only if for every open neighborhood U of p, there exists an N such that for all n >= N, p_n is in U.

In other words, no matter what neighborhood of p you give me, the "tail end" of the sequence is completely contained in that neighborhood.

2. Adjoined means to put them together. So my new cover is

He's just extending the cover to include the entire space you're working in.

"In the real world, this would be a problem. But in mathematics, we can just define a place where this problem doesn't exist. So we'll go ahead and do that now..."

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**Dragonshade****Member**- Registered: 2008-01-16
- Posts: 147

That explains it very clearly, Thanks guys

*Last edited by Dragonshade (2010-06-25 09:42:10)*

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