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## Open or Close, neither, or both?

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• Determine whether the given sets are open, closed, neither open nor closed, or both open and closed. 1. the union of all the closed intervals [-1+1/n, 1-1/n],
Message 1 of 5 , Sep 1, 2008
Determine whether the given sets are open, closed, neither open nor
closed, or both open and closed.

1. the union of all the closed intervals [-1+1/n, 1-1/n], n=2,3,...
2. the intersection of all the open intervals (0,(n+1)/n)

My guess:
1. open only
2. open only
• Hello , me too i guess that the two sets are open If you judge people, you have no time to love them Mother Teresa ... De: Michelle Wynne
Message 2 of 5 , Sep 1, 2008
Hello , me too i guess that the two sets are open

"If you judge people, you have no time to love them"

Mother Teresa

--- En date de : Lun 1.9.08, Michelle Wynne <michwynne@...> a écrit :
De: Michelle Wynne <michwynne@...>
Objet: [MATH for FUN] Open or Close, neither, or both?
À: mathforfun@yahoogroups.com
Date: Lundi 1 Septembre 2008, 9h11

Determine whether the given sets are open, closed, neither open nor
closed, or both open and closed.

1. the union of all the closed intervals [-1+1/n, 1-1/n], n=2,3,...
2. the intersection of all the open intervals (0,(n+1)/n)

My guess:
1. open only
2. open only

------------------------------------

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[Non-text portions of this message have been removed]
• [-1+1/n,1-1/n] is a closed set but the enumerable union of a closed set is not always closed and this union tends to ]-1,1[ so it s an opened set the
Message 3 of 5 , Sep 1, 2008
[-1+1/n,1-1/n] is a closed set but the enumerable union of a closed set is not always closed and this union tends to ]-1,1[ so it's an opened set
the enumerable  intersection of an open set is an open set so the second one is open

"If you judge people, you have no time to love them"

Mother Teresa

--- En date de : Lun 1.9.08, Michelle Wynne <michwynne@...> a écrit :
De: Michelle Wynne <michwynne@...>
Objet: [MATH for FUN] Open or Close, neither, or both?
À: mathforfun@yahoogroups.com
Date: Lundi 1 Septembre 2008, 9h11

Determine whether the given sets are open, closed, neither open nor
closed, or both open and closed.

1. the union of all the closed intervals [-1+1/n, 1-1/n], n=2,3,...
2. the intersection of all the open intervals (0,(n+1)/n)

My guess:
1. open only
2. open only

------------------------------------

_____________________________________________________________________________
Envoyez avec Yahoo! Mail. Une boite mail plus intelligente http://mail.yahoo.fr

[Non-text portions of this message have been removed]
• See the first exercises of chapter 2 in bartle: elements of Lebesgue integration for clues. Michelle Wynne escreveu: Determine
Message 4 of 5 , Sep 1, 2008
See the first exercises of chapter 2 in bartle: elements of Lebesgue integration for clues.

Michelle Wynne <michwynne@...> escreveu: Determine whether the given sets are open, closed, neither open nor
closed, or both open and closed.

1. the union of all the closed intervals [-1+1/n, 1-1/n], n=2,3,...
2. the intersection of all the open intervals (0,(n+1)/n)

My guess:
1. open only
2. open only

---------------------------------
Novos endereços, o Yahoo! que você conhece. Crie um email novo com a sua cara @... ou @....

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• ... set is not always closed and this union tends to ]-1,1[ so it s an opened set ... second one is open I think the intersection of a *finite* number of open
Message 5 of 5 , Sep 1, 2008
--- In mathforfun@yahoogroups.com, Ahlem <is.dreams@...> wrote:
>
> [-1+1/n,1-1/n] is a closed set but the enumerable union of a closed
set is not always closed and this union tends to ]-1,1[ so it's an
opened set
> the enumerableÂ  intersection of an open set is an open set so the
second one is open

I think the intersection of a *finite* number of open sets is always
open, but this (infinite) intersection is the half open interval
(0,1] neither open nor closed.

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> "If you judge people, you have no time to love them"
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> Mother Teresa
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> --- En date deÂ : Lun 1.9.08, Michelle Wynne <michwynne@...> a
> De: Michelle Wynne <michwynne@...>
> Objet: [MATH for FUN] Open or Close, neither, or both?
> Ã: mathforfun@yahoogroups.com
> Date: Lundi 1 Septembre 2008, 9h11
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> Determine whether the given sets are open, closed, neither open nor
> closed, or both open and closed.
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> 1. the union of all the closed intervals [-1+1/n, 1-1/n], n=2,3,...
> 2. the intersection of all the open intervals (0,(n+1)/n)
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> My guess:
> 1. open only
> 2. open only
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> Envoyez avec Yahoo! Mail. Une boite mail plus intelligente
http://mail.yahoo.fr
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> [Non-text portions of this message have been removed]
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